
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:

$$
\begin{aligned}
x^2 + 7y + 2 &= 2z + 4\sqrt{7x - 3} \\
y^2 + 7z + 2 &= 2x + 4\sqrt{7y - 3} \\
z^2 + 7x + 2 &= 2y + 4\sqrt{7z - 3}
\end{aligned}
$$

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