
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
Calculate the product of the complex numbers \((4 \operatorname{cis} 20^\circ)\) and \((-3\operatorname{cis} 45^\circ)\) in polar form, denoted as \(r \operatorname{cis} \theta\), where \(r > 0\) and \(0^\circ \leq \theta < 360^\circ\). Enter the ordered pair \((r, \theta)\).

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