
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 inequality $\log _{2}(x+2)\leqslant \log _{2}(8-2x)$.  
$(1)$ Find the solution set $A$ of the inequality.  
$(2)$ If the inequality ${(\frac{1}{4})}^{x-1}-4{(\frac{1}{2})}^{x}+2≥m$ holds for $x\in A$, find the range of values for $m$.

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