You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


/**************************************************************************//**
*   @file   adf4156.c
*   @brief  Implementation of ad9833 Driver for Microblaze processor.
*   @author Lucian Sin (<PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>)
*******************************************************************************
* Copyright 2013(c) Analog Devices, Inc.
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*  - Redistributions of source code must retain the above copyright
*    notice, this list of conditions and the following disclaimer.
*  - Redistributions in binary form must reproduce the above copyright
*    notice, this list of conditions and the following disclaimer in
*    the documentation and/or other materials provided with the
*    distribution.
*  - Neither the name of Analog Devices, Inc. nor the names of its
*    contributors may be used to endorse or promote products derived
*    from this software without specific prior written permission.
*  - The use of this software may or may not infringe the patent rights
*    of one or more patent holders.  This license does not release you
*    from the requirement that you obtain separate licenses from these
*    patent holders to use this software.
*  - Use of the software either in source or binary form, must be run
*    on or directly connected to an Analog Devices Inc. component.
*
* THIS SOFTWARE IS PROVIDED BY ANALOG DEVICES "AS IS" AND ANY EXPRESS OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, NON-INFRINGEMENT, MERCHANTABILITY
* AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL ANALOG DEVICES BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* INTELLECTUAL PROPERTY RIGHTS, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*******************************************************************************/

/******************************************************************************/
/***************************** Include Files **********************************/
/******************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include "adf4156.h"
#include "adf4156_cfg.h"

/***************************************************************************//**
 * @brief Initialize the SPI communication with the device.
 *
 * @param device     - The device structure.
 * @param init_param - The structure that contains the device initial
 * 		       parameters.
 *
 * @return status - Result of the initialization procedure.
 *                  Example:  0 - if initialization was successful;
 *                           -1 - if initialization was unsuccessful.
*******************************************************************************/
int8_t adf4156_init(struct adf4156_dev **device,
		    struct adf4156_init_param init_param)
{
	struct adf4156_dev *dev;
	uint32_t cfg_value;
	int8_t status;

	dev = (struct adf4156_dev *)malloc(sizeof(*dev));
	if (!dev)
		return -1;

	/* Setup GPIO pads */
	status = gpio_get(&dev->gpio_le, &init_param.gpio_le);
	status |= gpio_get(&dev->gpio_ce, &init_param.gpio_ce);

	/* Setup Control GPIO Pins */
	ADF4156_LE_OUT;
	ADF4156_LE_LOW;
	ADF4156_CE_OUT;
	ADF4156_CE_HIGH;
	//ADF4156_LE2_OUT;
	//ADF4156_CE2_OUT;

	/* Setup SPI Interface */
	status |= spi_init(&dev->spi_desc, &init_param.spi_init);

	/* R4 */
	cfg_value = adf4156_pdata_lpc.r4_user_settings |
		    ADF4156_R4_CTRL;
	adf4156_set(dev,
		    cfg_value);
	dev->adf4156_st.reg_val[ADF4156_REG4] = cfg_value;

	/* R3 */
	cfg_value = adf4156_pdata_lpc.r3_user_settings |
		    ADF4156_R3_CTRL;
	adf4156_set(dev,
		    cfg_value);
	dev->adf4156_st.reg_val[ADF4156_REG3] = cfg_value;

	/* R2 */
	cfg_value = adf4156_pdata_lpc.r2_user_settings |
		    ADF4156_PRESCALER(0)               |
		    (adf4156_pdata_lpc.ref_div2_en ? ADF4156_RDIV2(1) : ADF4156_RDIV2(0))        |
		    (adf4156_pdata_lpc.ref_doubler_en ? ADF4156_REF_DBL(1) : ADF4156_REF_DBL(0)) |
		    ADF4156_R_CNT(1)                   |
		    ADF4156_MOD_WORD(0)                |
		    ADF4156_R2_CTRL;
	adf4156_set(dev,
		    cfg_value);
	dev->adf4156_st.reg_val[ADF4156_REG2] = cfg_value;

	/* R1 */
	cfg_value = ADF4156_PHASE_VAL(1)     |
		    ADF4156_R1_CTRL;
	adf4156_set(dev,
		    cfg_value);
	dev->adf4156_st.reg_val[ADF4156_REG1] = cfg_value;

	/* R0 */
	cfg_value = adf4156_pdata_lpc.r0_user_settings |
		    ADF4156_INT_VAL(1)                 |
		    ADF4156_FRAC_VAL(1)                |
		    ADF4156_R0_CTRL;
	adf4156_set(dev,
		    cfg_value);
	dev->adf4156_st.reg_val[ADF4156_REG0] = cfg_value;

	*device = dev;

	return status;
}

/***************************************************************************//**
 * @brief Free the resources allocated by adf4156_init().
 *
 * @param dev - The device structure.
 *
 * @return SUCCESS in case of success, negative error code otherwise.
*******************************************************************************/
int32_t adf4156_remove(struct adf4156_dev *dev)
{
	int32_t ret;

	ret = spi_remove(dev->spi_desc);

	ret |= gpio_remove(dev->gpio_le);
	ret |= gpio_remove(dev->gpio_ce);

	free(dev);

	return ret;
}

/**************************************************************************//**
 * @brief Transmits 32 bits on SPI.
 *
 * @param dev   - The device structure.
 * @param value - Data which will be transmitted.
 *
 * @return none.
******************************************************************************/
int8_t adf4156_set(struct adf4156_dev *dev,
		   uint32_t value)
{
	int8_t validation = 0;
	int8_t status = 0;
	uint8_t tx_buffer[4] = {0, 0, 0, 0};// TX SPI Buffer

	tx_buffer[0] = (uint8_t)((value & 0xFF000000) >> 24);
	tx_buffer[1] = (uint8_t)((value & 0x00FF0000) >> 16);
	tx_buffer[2] = (uint8_t)((value & 0x0000FF00) >> 8);
	tx_buffer[3] = (uint8_t)((value & 0x000000FF) >> 0);

	ADF4156_LE_LOW;
	validation = spi_write_and_read(dev->spi_desc,
					tx_buffer,
					4);
	if (validation != 4) {
		status = -1;
	}
	ADF4156_LE_HIGH;

	return status;
}

/***************************************************************************//**
 * @brief Increases the R counter value until the PFD frequency is
 *        smaller than ADF4351_MAX_FREQ_PFD.
 *
 * @param dev   - The device structure.
 * @param r_cnt - Initial r_cnt value.
 *
 * @return Final r_cnt value.
*******************************************************************************/
int32_t adf4156_tune_r_cnt(struct adf4156_dev *dev,
			   int32_t r_cnt)
{
	struct adf4156_platform_data *pdata = dev->adf4156_st.pdata;

	do {
		r_cnt++;
		dev->adf4156_st.fpfd = (pdata->clkin * \
					(pdata->ref_doubler_en ? 2 : 1)) /
				       (r_cnt * (pdata->ref_div2_en ? 2 : 1));
	} while (dev->adf4156_st.fpfd > ADF4156_MAX_FREQ_PFD);

	return r_cnt;
}

/***************************************************************************//**
 * @brief Computes the greatest common divider of two numbers.
 *
 * @return Returns the gcd.
*******************************************************************************/
uint32_t gcd(uint32_t x, uint32_t y)
{
	uint32_t tmp;

	while (y != 0) {
		tmp = x % y;
		x = y;
		y = tmp;
	}

	return x;
}

/***************************************************************************//**
 * @brief Sets the ADF4156 output frequency.
 *
 * @param dev     - The device structure.
 * @param freq    - The desired frequency value.
 *
 * @return calculatedFrequency - The actual frequency value that was set.
*******************************************************************************/
double adf4156_set_freq(struct adf4156_dev *dev,
			double freq)
{
	uint64_t tmp;
	uint32_t       div_gcd, prescaler, chspc;
	uint16_t mdiv;
	uint16_t r_cnt = 0;
	double result;


	if ((freq > ADF4156_MAX_OUT_FREQ) || (freq < ADF4156_MIN_OUT_FREQ)) {
		return -1;
	}
	if (freq > ADF4156_MAX_FREQ_45_PRESC) {
		prescaler = ADF4156_PRESCALER(1);
		mdiv = 75;
	} else {
		prescaler = ADF4156_PRESCALER(0);
		mdiv = 23;
	}

	freq *= 1000000;
	chspc = dev->adf4156_st.pdata->channel_spacing;

	if ((dev->adf4156_st.pdata->clkin > ADF4156_MAX_FREQ_REFIN) ||
	    (dev->adf4156_st.pdata->clkin < ADF4156_MIN_FREQ_REFIN)) {
		return -1;
	}

	do {
		do {
			r_cnt = adf4156_tune_r_cnt(dev, r_cnt);
			dev->adf4156_st.r2_mod = \
						 dev->adf4156_st.fpfd / chspc;
			if (r_cnt > ADF4156_MAX_R_CNT) {
				printf("Error! R-counter has a too high \
value for the selected spacing. Try with a higher spacing value.\r\n");
				return -1;
			}
		} while ((dev->adf4156_st.r2_mod > ADF4156_MAX_MODULUS) && r_cnt);
		dev->adf4156_st.r_cnt = r_cnt;
		tmp = freq * (uint64_t)dev->adf4156_st.r2_mod + (dev->adf4156_st.fpfd >> 1);
		tmp = (uint64_t)(tmp / dev->adf4156_st.fpfd);
		dev->adf4156_st.r0_fract = tmp % dev->adf4156_st.r2_mod;
		tmp = tmp / dev->adf4156_st.r2_mod;
		dev->adf4156_st.r0_int = (uint32_t)tmp;
	} while (mdiv > dev->adf4156_st.r0_int);

	if (dev->adf4156_st.r0_fract && dev->adf4156_st.r2_mod) {
		div_gcd = gcd(dev->adf4156_st.r2_mod,
			      dev->adf4156_st.r0_fract);
		dev->adf4156_st.r2_mod /= div_gcd;
		dev->adf4156_st.r0_fract /= div_gcd;
	} else {
		dev->adf4156_st.r0_fract = 0;
		dev->adf4156_st.r2_mod = 1;
	}

	/* register R3 */
	dev->adf4156_st.reg_val[ADF4156_REG3] &= ~(ADF4156_CNT_RST(-1));
	dev->adf4156_st.reg_val[ADF4156_REG3] |= (ADF4156_CNT_RST(1));

	adf4156_set(dev,
		    dev->adf4156_st.reg_val[ADF4156_REG3]);

	/* register R2 */
	dev->adf4156_st.reg_val[ADF4156_REG2] &= ~(ADF4156_MOD_WORD(-1) |
			ADF4156_R_CNT(-1)    |
			ADF4156_PRESCALER(-1));
	dev->adf4156_st.reg_val[ADF4156_REG2] |= (ADF4156_MOD_WORD(
				dev->adf4156_st.r2_mod) |
			ADF4156_R_CNT(dev->adf4156_st.r_cnt)     |
			prescaler);
	adf4156_set(dev,
		    dev->adf4156_st.reg_val[ADF4156_REG2]);

	/* register R0 */
	dev->adf4156_st.reg_val[ADF4156_REG0] &= ~(ADF4156_INT_VAL(-1) |
			ADF4156_FRAC_VAL(-1));
	dev->adf4156_st.reg_val[ADF4156_REG0] |= (ADF4156_INT_VAL(
				dev->adf4156_st.r0_int) |
			ADF4156_FRAC_VAL(dev->adf4156_st.r0_fract));
	adf4156_set(dev,
		    dev->adf4156_st.reg_val[ADF4156_REG0]);

	/* register R3 */
	dev->adf4156_st.reg_val[ADF4156_REG3] &= ~(ADF4156_CNT_RST(-1));
	adf4156_set(dev,
		    dev->adf4156_st.reg_val[ADF4156_REG3]);

	result = dev->adf4156_st.r0_int * (float)(dev->adf4156_st.fpfd / 1000000);
	result = result + ((float)dev->adf4156_st.r0_fract / dev->adf4156_st.r2_mod) *\
		 (dev->adf4156_st.fpfd / 1000000);

	return result;
}