
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
Solve the following system of equations:

$$
\begin{gathered}
\left(x^{2}+11\right) \sqrt{21+y^{2}}=180, \quad\left(y^{2}+21\right) \sqrt{z^{2}-33}=100 \\
\left(z^{2}-33\right) \sqrt{11+x^{2}}=96
\end{gathered}
$$

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