
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
Let the complex number $z$ satisfies the equation $z + |z| = 3 + 7i$. Determine the value of $|z|^{2}$.
A) $\frac{600}{9}$
B) $\frac{841}{9}$
C) $\frac{500}{9}$
D) $\frac{960}{9}$
E) $\frac{900}{9}$

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