
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
Assuming \( \boldsymbol{x} \) and \( \boldsymbol{y} \) are integers, solve the system of equations:
$$
\left\{\begin{array}{l}
4^{x^{2}+2 x y+1}=(z+2) 7^{|y|-1} \\
\sin \frac{3 \pi z}{2}=1
\end{array}\right.
$$

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