
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: $3\tan 45^{\circ}-\left(\frac{1}{3}\right)^{-1}+\left(\sin 30^{\circ}-2022\right)^{0}+|\cos 30^{\circ}-\frac{\sqrt{3}}{2}|$.  
$(2)$ Solve the equation: $x(x+3)=5(x+3)$.

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