
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
Given the complex number $z$ that satisfies: $|z|=1+3i-z$,
(1) Find $z$ and the coordinates of the corresponding point on the complex plane;
(2) Find the conjugate of $\frac{(1+i)^{2}(3+4i)^{2}}{2z}$.

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