
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 $f(x)=|x|-\cos x$, for any $x\_1$, $x\_2$ in the interval $[-π,π]$, the following conditions are provided:
\[①x\_1 > |x\_2|;\] \[②|x\_1| > x\_2;\] \[③x\_1^2 > x\_2^2;\] \[④x\_1^3 > x\_2^3\]
Determine the sequence number(s) of the condition(s) that always ensure $f(x\_1) > f(x\_2)$. (Write out the sequence number(s) only)

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