You will receive a question-answer pair. Your task is to:

1. Decompose the answer into a sequence of numbered steps ("Step 1", "Step 2", etc.).
2. For each step, include a reasoning description and assign a confidence score (a float between 0 and 1).
3. For **accepted answers**, ensure reasoning steps are correct, with confidence scores that progressively increase as the steps approach the final answer.
4. For **rejected answers**, introduce flaws or errors in reasoning steps, and use inconsistent or lower confidence scores.

Please output the response in the JSON format below, following the example provided.


---

*Expected JSON Output Format:*

{
  "question": "[Insert question text here]",
  "accepted_answer": {
    "Step 1": {
      "reasoning": "[Describe the first reasoning step here]",
      "confidence_score": [Float between 0 and 1, e.g., 0.7]
    },
    "Step 2": {
      "reasoning": "[Describe the next reasoning step]",
      "confidence_score": [Incrementally higher float, e.g., 0.8]
    },
    "Step 3": {
      "reasoning": "[Continue describing each step with incrementally higher scores]",
      "confidence_score": [Approaching 1, e.g., 0.9]
    }
    // Continue until the final reasoning step
  },
  "rejected_answer": {
    "Step 1": {
      "reasoning": "[Introduce an incorrect or misleading reasoning step here]",
      "confidence_score": [Lower or inconsistent float, e.g., 0.5]
    },
    "Step 2": {
      "reasoning": "[Add a flawed or irrelevant reasoning step]",
      "confidence_score": [Inconsistent or lower float, e.g., 0.4]
    },
    "Step 3": {
      "reasoning": "[Continue with errors or inconsistencies in reasoning]",
      "confidence_score": [Non-incremental or lower float, e.g., 0.6]
    }
    // Continue until the final flawed reasoning step
  }
}

---

*Example JSON Output:*

{
  "question": "What are the primary causes of climate change?",
  "accepted_answer": {
    "Step 1": {
      "reasoning": "Identify human activities as significant contributors to climate change.",
      "confidence_score": 0.7
    },
    "Step 2": {
      "reasoning": "Specify fossil fuel burning as a major source of greenhouse gases.",
      "confidence_score": 0.8
    },
    "Step 3": {
      "reasoning": "Explain how deforestation reduces CO2 absorption, increasing atmospheric CO2.",
      "confidence_score": 0.9
    }
  },
  "rejected_answer": {
    "Step 1": {
      "reasoning": "Suggest natural factors as primary contributors to climate change.",
      "confidence_score": 0.5
    },
    "Step 2": {
      "reasoning": "Mention volcanic activity as a significant greenhouse gas source, incorrect for recent climate trends.",
      "confidence_score": 0.4
    },
    "Step 3": {
      "reasoning": "Briefly describe human activities without identifying specific sources.",
      "confidence_score": 0.6
    }
  }
}

Question: In the diagram, $F$ is the midpoint of $\overline{CD}$, and $G$ is the midpoint of $\overline{AB}$. Determine the sum of the $x$ and $y$ coordinates of $H$, the point of intersection of $\overline{FG}$ and $\overline{AE}$. [asy]
size(180); defaultpen(linewidth(.7pt)+fontsize(10pt));
pair A, B, C, D, E, F, G, H;
A=(0,6);
B=(0,0);
C=(8,0);
D=(0,3);
E=(4,0);
F=(8/3,1);
G=(0,3);
H=(2,2);
draw(E--A--C--D);
draw(F--G);
draw((-1,0)--(10,0), EndArrow);
draw((0,-1)--(0,8), EndArrow);
label("$A(0,6)$", A, W);
label("$B(0,0)$", B, SW);
label("$C(8,0)$", C, S);
label("$D$", D, W);
label("$E$", E, S);
label("$F$", F, SW);
label("$G$", G, W);
label("$H$", H, SW);
label("$x$", (10,0), dir(0));
label("$y$", (0,8), dir(90));
[/asy]
Answer: Since $F$ is the midpoint of $\overline{CD}$ and $G$ is the midpoint of $\overline{AB}$, we can use the midpoint formula to find their coordinates.

The midpoint formula is:
\[ M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]

For $F$, the midpoint of $\overline{CD}$:
\[ F = \left(\frac{8 + 0}{2}, \frac{0 + 3}{2}\right) = (4, 1.5) \]

For $G$, the midpoint of $\overline{AB}$:
\[ G = \left(\frac{0 + 0}{2}, \frac{6 + 0}{2}\right) = (0, 3) \]

Now, we need to find the equation of the line passing through $F$ and $G$. We can use the slope-intercept form:
\[ y = mx + b \]

First, find the slope $m$:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1.5}{0 - 4} = \frac{1.5}{-4} = -\frac{3}{8} \]

Next, find the $y$-intercept $b$. We can use the coordinates of $G$ since it lies on the $y$-axis:
\[ b = 3 \]

So, the equation of the line is:
\[ y = -\frac{3}{8}x + 3 \]

Now, we need to find the point of intersection $H$ of this line and $\overline{AE}$. The line $\overline{AE}$ passes through points $A(0, 6)$ and $E(4, 0)$. We can find its equation as well.

First, find the slope $m_{AE}$:
\[ m_{AE} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 6}{4 - 0} = \frac{-6}{4} = -\frac{3}{2} \]

Next, find the $y$-intercept $b_{AE}$. We can use the coordinates of $A$ since it lies on the $y$-axis:
\[ b_{AE} = 6 \]

So, the equation of the line $\overline{AE}$ is:
\[ y = -\frac{3}{2}x + 6 \]

To find the point of intersection $H$, we can set the two equations equal to each other and solve for $x$:
\[ -\frac{3}{8}x + 3 = -\frac{3}{2}x + 6 \]

Multiply both sides by 8 to eliminate the fractions:
\[ -3x + 24 = -12x + 48 \]

Add $12x$ to both sides:
\[ 9x + 24 = 48 \]

Subtract 24 from both sides:
\[ 9x = 24 \]

Divide both sides by 9:
\[ x = \frac{24}{9} = \frac{8}{3} \]

Now that we have $x$, we can substitute it into one of the line equations to find $y$. Let's use the equation of the line passing through $F$ and $G$:
\[ y = -\frac{3}{8}\left(\frac{8}{3}\right) + 3 = -1 + 3 = 2 \]

So, the coordinates of $H$ are $\left(\frac{8}{3}, 2\right)$.

The sum of the $x$ and $y$ coordinates of $H$ is:
\[ \frac{8}{3} + 2 = \frac{8}{3} + \frac{6}{3} = \frac{14}{3} \]

The answer is:
\[ \boxed{\frac{14}{3}} \]