
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 functions $y=f(x)$ and $y=g(x)$, whose graphs are shown on the right within the interval $[-2,2]$, the equation $f[g(x)]=0$ has exactly \_\_\_\_ roots;  
the equation $f[f(x)]=0$ has exactly \_\_\_\_ roots.

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