
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 $\sqrt{4} + \sqrt{(-2)^2} + \sqrt{\frac{9}{4}} - \left( \sqrt{\frac{1}{2}} \right)^2 + \sqrt[3]{-125}$

(2) Solve the equation using square roots: $(2x-1)^2 - 169 = 0$;

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