
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 on  $\mathbb{R}$ , such that  $f(x)=x^2$  when  $x\ge 0$ . Knowing that for all  $x\in [a,a+2]$ , the inequality  $f(x+a)\ge 2f(x)$  holds, find the range of real number  $a$ .

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