
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 $a$ is a real number and $a \neq 1$, the function $f(x)$ is defined as follows:

$$
f(x) =
\begin{cases}
4^{x}, & x \geq 0, \\
2^{a - x}, & x < 0.
\end{cases}
$$
Find the value of $a$ such that $f(1 - a) = f(a - 1)$.

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