
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 $f(x)= \begin{cases} x^{2}+2x, & -2\leqslant x\leqslant 0 \\ f(x-1)+1, & 0 < x\leqslant 2 \end{cases}$, determine the number of roots of the equation $x-f(x)=0$ in the interval $[-2,2]$.

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