
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
$(1)$ Simplify: $(2-\frac{x-1}{x+2})\div \frac{{x}^{2}+10x+25}{{x}^{2}-4}$;<br/>$(2)$ Solve the inequality system: $\left\{\begin{array}{l}2x+7>3\\ \frac{x+1}{3}>\frac{x-1}{2}\end{array}\right.$.

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