
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 $A_0=(0,0)$. Distinct points $A_1, A_2, \dots$ lie on the $x$-axis, and distinct points $B_1, B_2, \dots$ lie on the graph of $y=x^2$. For every positive integer $n$, right triangle $A_{n-1}B_nA_n$ has $A_{n-1}B_n$ as the hypotenuse. What is the least $n$ for which the length $A_0A_n \geq 100$?

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