
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
Calculate:<br/>$(1)$ Calculate: $|1-\sqrt{3}|-\sqrt{27}+2×\frac{\sqrt{3}}{2}+(\frac{1}{2})^{-2}$;<br/>$(2)$ Solve the equation: $2x^{2}-5x-1=0$;<br/>$(3)$ Simplify first, then find the value of: $(2a-\frac{12a}{a+2})÷\frac{a-4}{a^{2}+4a+4}$, where $a$ satisfies $a^{2}+2a-5=0$.

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