
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 \(\mathbf{R}\), and \( f(x) = x^{2} \) when \( x \geqslant 0 \). If the inequality \( f(x+a) \geqslant 2 f(x) \) holds for any \( x \in [a, a+2] \), find the range of the real number \( a \).

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