
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 $f(x)=\sin ^{6}x+\cos ^{6}x$, provide the following conclusions:
  1. The range of $f(x)$ is $[0,2]$;
  2. The smallest positive period of $f(x)$ is $\frac{\pi}{2}$;
  3. The equation of the symmetry axis of the graph of $f(x)$ is $x=\frac{k\pi}{4}(k\in\mathbb{Z})$;
  4. The center of symmetry of the graph of $f(x)$ is $(\frac{\pi}{8}+\frac{k\pi}{4},\frac{5}{8})(k\in\mathbb{Z})$

Write the sequence numbers of all correct conclusions.

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