
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
$(1)$ Calculate: $(\frac{1}{2})^{-1}-2\tan 45^{\circ}+|1-\sqrt{2}|$;<br/>$(2)$ Simplify first: $(\frac{a}{{{a^2}-4}}+\frac{1}{{2-a}})\div \frac{{2a+4}}{{{a^2}+4a+4}}$, then find the value, where $a=\sqrt{3}+2$.

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