
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 that $m$ and $n$ are real numbers, if $\log_{2}(m^{2}-3m-3)+i\log_{2}(m-2)$ is a purely imaginary number, and the corresponding point of the complex number $z=m+ni$ is on the line $x+y-2=0$, then $|z|=$________.

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