
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
Let the domains of the functions $f(x)$ and $g(x)$ be $D_f$ and $D_g$, respectively, and $D_f \subseteq D_g$. If for any $x \in D_f$, we have $g(x) = f(x)$, then the function $g(x)$ is called an extension of $f(x)$ on $D_g$. Suppose $f(x) = 2^x$ (for $x \leq 0$), and $g(x)$ is an extension of $f(x)$ on $\mathbb{R}$, and $g(x)$ is an even function, then $g(x) = \boxed{2^{-|x|}}$.

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