
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 the real numbers \(a_1, a_2, \cdots, a_{100}\) satisfy the following conditions: (i) \(a_1 \geq a_2 \geq \cdots \geq a_{100} \geq 0\); (ii) \(a_1 + a_2 \leq 100\); (iii) \(a_3 + a_4 + \cdots + a_{100} \leq 100\). Find the maximum value of \(a_1^2 + a_2^2 + \cdots + a_{100}^2\) and the values of \(a_1, a_2, \cdots, a_{100}\) that achieve this maximum.

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