
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

Let \( p_{i} \) be the \(i^{\text {th }}\) prime number; for example, \( p_{1}=2, p_{2}=3 \), and \( p_{3}=5 \). For each prime number, construct the point \( Q_{i}\left(p_{i}, 0\right) \). Suppose \( A \) has coordinates \((0,2)\). Determine the sum of the areas of the triangles \(\triangle A Q_{1} Q_{2}, \triangle A Q_{2} Q_{3}, \triangle A Q_{3} Q_{4}, \triangle A Q_{4} Q_{5}, \triangle A Q_{5} Q_{6}, \) and \(\triangle A Q_{6} Q_{7}\).

Present the answer in LaTex format: \boxed{Your answer}
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