
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) \(a_{1} \geqslant a_{2} \geqslant \cdots \geqslant a_{100} \geqslant 0\); (ii) \(a_{1}+a_{2} \leqslant 100\); (iii) \(a_{3}+a_{4} + \cdots + a_{100} \leqslant 100\). Find the maximum value of \(a_{1}^{2}+a_{2}^{2}+\cdots+a_{100}^{2}\) and the values of \(a_{1}, a_{2}, \cdots, a_{100}\) when the maximum value is reached.

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