
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
Circle $\odot C_{1}$ is inscribed in a parabola. Circle $\odot C_{2}$ is externally tangent to $\odot C_{1}$ and also inscribed in the parabola. Circle $\odot C_{3}$ is externally tangent to $\odot C_{2}$ and also inscribed in the parabola, and so on. Given a sequence of circles $C_{1}, C_{2}, C_{3}, \cdots$, find the sum of the areas of the first $n$ circles.

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