
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 set $A=\left{ x\mid x\leqslant 0 \right}$, and a mapping ${{f}_{\,}}:A\to B$ with the corresponding rule ${{f}_{\,}}:x\to {{2}^{x}}$, determine the element in set $A$ that corresponds to the element $\frac{1}{8}$ in set $B$.

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