
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
Inside the parabola \(y = x^2\), there are non-overlapping circles \(\omega_1, \omega_2, \omega_3, \ldots\) such that for each \(n > 1\), the circle \(\omega_n\) touches the branches of the parabola and externally touches the circle \(\omega_{n-1}\). Find the radius of the circle \(\omega_{1998}\) given that the diameter of \(\omega_1\) is 1 and it touches the parabola at its vertex.

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