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

$$
f(x) =
\begin{cases}
4^{x}, & \text{when } x \geq 0 \\
2^{a-x}, & \text{when } x < 0
\end{cases}
$$

If $f(1-a) = f(a-1)$, find the value of $a$.

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