
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 $f(x)=(\frac{1}{2})^{ax}$, where $a$ is a constant and the graph of the function passes through the point $(-1,2)$.
$(1)$ Find the value of $a$;
$(2)$ If $g(x)=4^{-x}-2$ and $g(x)=f(x)$, find the value of $x$ that satisfies the condition.

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