
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
$(1)\sqrt[3]{-64}+\sqrt{16}×\sqrt{\frac{9}{4}}+(-\sqrt{2})^{2}$；<br/>$(2)|1-\sqrt{2}|+|\sqrt{2}-2|-|\pi -3|$；<br/>$(3)\left(2x-1\right)^{2}-25=0$；<br/>$(4)\left(x+1\right)^{2}-25=0$.

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