
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 that $a \neq 0$ is a real number, the function $f(x)$ is defined as follows:
$$
f(x) = \begin{cases}
2x + a, & x < 1 \\
-x - 2a, & x \geq 1
\end{cases}
$$
If $f(1 - a) = f(1 + a)$, find the value of $a$.

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