
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 \(a_1 \geq a_2 \geq \cdots \geq a_n > 0\) and \(\sum_{i=1}^{k} a_i \leq \sum_{i=1}^{k} b_i \) for \(1 \leq k \leq n\). Then:
(1) \(\sum_{i=1}^{n} a_i^2 \leq \sum_{i=1}^{n} b_i^2\);
(2) \(\sum_{i=1}^{n} a_i^3 \leq \sum_{i=1}^{n} a_i b_i^2\).

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