
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: $\sqrt{12}+|-4|-\left(2003-\pi \right)^{0}-2\cos 30^{\circ}$;<br/>$(2)$ Simplify first, then evaluate: $(a+2-\frac{5}{a-2})\div \frac{3-a}{2a-4}$, where $a$ is an integer satisfying $0 \lt a \lt 4$.

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