use this template:
### Expanded Template for Deductive and Inductive Reasoning Using Scientific Theory
 
#### Deductive Reasoning Template
1. **Define the Theory or Principle:**
   - [State the overarching scientific theory or principle that will guide the reasoning process.]
   - Example: *Newton's Laws of Motion*
 
2. **Formulate a Hypothesis:**
   - [Derive a specific hypothesis or prediction based on the theory.]
   - Example: *If an object is in motion, it will remain in motion unless acted upon by an external force.*
 
3. **Identify Relevant Observations or Data:**
   - [List the observations or data that will be used to test the hypothesis.]
   - Example: *Observations of a rolling ball on a flat surface.*
 
4. **Apply Logical Reasoning:**
   - [Use logical steps to connect the theory to the hypothesis and observations.]
   - Example:
     - *Premise 1: According to Newton's First Law, an object in motion will remain in motion unless acted upon by an external force.*
     - *Premise 2: The rolling ball is an object in motion.*
     - *Conclusion: The rolling ball will continue to roll unless an external force (like friction) acts upon it.*
 
5. **Evaluate the Conclusion:**
   - [Assess whether the conclusion aligns with the observations and the theory.]
   - Example: *The rolling ball eventually stops due to friction, confirming Newton's First Law.*
 
6. **Refine the Hypothesis or Theory (if necessary):**
   - [Adjust the hypothesis or theory based on the evaluation.]
   - Example: *Include the effect of friction in the hypothesis.*
 
7. **Document the Reasoning Process:**
   - [Record the logical steps, observations, and conclusions for future reference.]
   - Example: *Write a report detailing the logical reasoning process and the results.*
 
8. **Communicate Findings:**
   - [Share the results with peers or the scientific community for feedback and validation.]
   - Example: *Present findings at a scientific conference or publish in a journal.*
 
#### Inductive Reasoning Template
1. **Gather Observations or Data:**
   - [Collect a series of observations or data points relevant to the scientific theory.]
   - Example: *Observations of various objects falling to the ground.*
 
2. **Identify Patterns or Trends:**
   - [Look for consistent patterns or trends in the collected data.]
   - Example: *All observed objects fall towards the ground when dropped.*
 
3. **Formulate a General Hypothesis:**
   - [Create a general hypothesis based on the identified patterns.]
   - Example: *All objects fall towards the ground due to gravity.*
 
4. **Test the Hypothesis:**
   - [Design experiments or gather additional data to test the hypothesis.]
   - Example: *Drop different objects from varying heights and observe their behavior.*
 
5. **Refine the Hypothesis:**
   - [Adjust the hypothesis based on the results of the tests.]
   - Example: *Include the effect of air resistance in the hypothesis.*
 
6. **Develop a Theory:**
   - [Formulate a broader scientific theory that explains the refined hypothesis.]
   - Example: *Theory of Gravity: All objects are attracted towards the Earth due to gravitational force.*
 
7. **Apply the Theory to New Observations:**
   - [Use the theory to predict and explain new observations.]
   - Example: *Predict that a feather will fall slower than a stone due to air resistance.*
 
8. **Evaluate and Refine the Theory:**
   - [Continuously assess the theory against new data and refine it as necessary.]
   - Example: *Incorporate the concept of gravitational acceleration in the theory.*
 
9. **Document the Reasoning Process:**
   - [Record the logical steps, observations, and conclusions for future reference.]
   - Example: *Write a report detailing the logical reasoning process and the results.*
 
10. **Communicate Findings:**
    - [Share the results with peers or the scientific community for feedback and validation.]
    - Example: *Present findings at a scientific conference or publish in a journal.*
 
### Command Terms Glossary
- **Define:** Provide a clear and concise explanation of a concept or term.
- **Formulate:** Create or develop a hypothesis or theory based on available information.
- **Identify:** Recognize and list relevant data, patterns, or trends.
- **Apply:** Use a theory or principle to explain or predict phenomena.
- **Evaluate:** Assess the validity or reliability of a hypothesis, theory, or conclusion.
- **Refine:** Adjust or improve a hypothesis or theory based on new evidence.
- **Test:** Conduct experiments or gather data to verify a hypothesis.
- **Develop:** Build or expand a theory based on refined hypotheses.
- **Document:** Record the logical steps, observations, and conclusions for future reference.
- **Communicate:** Share findings with peers or the scientific community for feedback and validation.
**Note**: Code/Python/Calculators are not applicable in verifying answers unless the answer pertains to creating such elements.
 
### user query ###
What's the long diagonal of a regular hexagon with the short diagonal of 64?

Before starting your template, provide your reasoning in latin.