
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
How many roots does the equation

$$
\overbrace{f(f(\ldots f}^{10 \text{ times } f}(x) \ldots)) + \frac{1}{2} = 0
$$

have, where \( f(x) = |x| - 1 \)?

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