
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 $f(x)$ whose domain is $\mathbb{R}$, when $x < 0$, $f(x) = x^3 - 1$; when $-1 \leqslant x \leqslant 1$, $f(-x) = -f(x)$; when $x > \frac{1}{2}$, $f\left(x+ \frac{1}{2}\right) = f\left(x- \frac{1}{2}\right)$. Evaluate $f(6)$.

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