
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 equation $z(z+i)(z+3i)(z-2)=180i$ and find the real part $a$ of a zero of the form $a+bi$, where $a$ and $b$ are positive real numbers.
A) $\sqrt{50}$
B) $2\sqrt{45}$
C) $\sqrt{180}$
D) $\sqrt{200}$
E) $\sqrt{90}$

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