
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
Given the function $f(x) = x^2 - 2\cos{x}$, for any $x_1$, $x_2$ in the interval $\left[- \frac {2\pi}{3},  \frac {2\pi}{3}\right]$, under the following conditions:
1. $x_1 > x_2$;      
2. $x_{1}^{2} > x_{2}^{2}$;
3. $x_1 > |x_2|$;
4. $|x_1| > x_2$;

Among these, the condition(s) that make $f(x_1) > f(x_2)$ always true is __________ (Fill in the number).

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