
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
In the plane Cartesian coordinate system \( xOy \), there are 2018 circles: \( \odot A_{1}, \odot A_{2}, \cdots, \odot A_{2018} \), where the center of circle \( \odot A_{k} \) is \( A_{k}\left(a_{k}, \frac{1}{4} a_{k}^{2}\right) \) and the radius is \( \frac{1}{4} a_{k}^{2} \) (for \( k = 1, \cdots, 2018 \)). Here, \( a_{1} > \cdots > a_{2018} = \frac{1}{2018} \), and circle \( \odot A_{k+1} \) is externally tangent to circle \( \odot A_{k} \) (for \( k = 1, 2, \cdots, 2017 \)). Find \( a_{1} = \) __________

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