
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 $f(x) = \begin{cases} -x-1 & (x < -1) \\ -x^2+1 & (-1 \leq x \leq 1) \\ x-1 & (x > 1) \end{cases}$.
1. Find $f(2)$ and $f(-2)$.
2. If $f(a) = 1$, find the value of the real number $a$.
3. Determine the parity of the function $f(x)$ (only write the result, no proof required).
4. Write down the intervals where the function is increasing or decreasing.

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