
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 $f(x)= \begin{cases} 2^{-x} & ,x < 1 \\\\ \log _{4}x & ,x\geqslant 1\\end{cases}$
(1) Find the solution(s) to the equation $f(x)= \dfrac {1}{4}$;
(2) Find the solution set for the inequality $F(x)\leqslant 2$.

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