
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 $f(x) = \begin{cases} 2^{x-4} & ,x\leqslant 4\\ -\log_{2}(x+1) & ,x > 4 \end{cases}$, solve for $a$ if $f(a) = \dfrac{1}{8}$.

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