
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
Let \[f(x) = \left\{
\begin{array}{cl}
2x + 3 & \text{if } x \le 1, \\
-3x + 6 & \text{if } x > 1.
\end{array}
\right.\] How many solutions does the equation \( f(f(x)) = 0 \) have?

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