
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

For \( x \) a real number, let \( f(x) = 0 \) if \( x < 1 \) and \( f(x) = 2x - 2 \) if \( x \geq 1 \). How many solutions are there to the equation
\[ 
f(f(f(f(x)))) = x ?
\]

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