
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 \( f(x) \) be an odd function defined on \( \mathbf{R} \), such that \( f(x) = x^2 \) for \( x \geqslant 0 \). If for any \( x \in [a, a+2] \), \( f(x+a) \geqslant 2 f(x) \), then determine the range of the real number \( a \).

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