
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
$(1)$ Solve the system of equations: $\left\{\begin{array}{l}5x+2y=25\\ 3x+4y=15\end{array}\right.$; <br/>$(2)$ Calculate: $2(\sqrt{3}-1)-|\sqrt{3}-2|-\sqrt[3]{-64}$; <br/>$(3)$ Solve the equation: $2\left(x-1\right)^{2}-49=1$.

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