
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
Given a sequence of real numbers \( a_{1}, a_{2}, a_{3}, \ldots \) that satisfy
1) \( a_{1}=\frac{1}{2} \), and
2) \( a_{1} + a_{2} + \ldots + a_{k} = k^{2} a_{k} \), for \( k \geq 2 \).
Determine the value of \( a_{100} \).

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