
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: $2\cos 30^{\circ}-\tan 60^{\circ}+\sin 30^{\circ}+|-\frac{1}{2}|$.  
$(2)$ Simplify first, then find the value: $1-\frac{a-b}{a+2b}\div \frac{{a}^{2}-{b}^{2}}{{a}^{2}+4ab+4{b}^{2}}$, where $a=2\sin 60^{\circ}-3\tan 45^{\circ}$, $b=3$.

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