
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
Simplify: $\frac{16-{a}^{2}}{{a}^{2}+8a+16}\div (\frac{1}{2}-\frac{4}{a+4})\cdot \frac{1}{2a-4}$, then choose a suitable integer $a$ from the solution set $\left\{\begin{array}{l}{\frac{1}{2}(a-1)＜2}\\{\frac{a+1}{2}≥\frac{4-a}{3}}\end{array}\right.$ to substitute and evaluate.

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