
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
Find the value of $C$ in the polynomial $z^6 - 21z^5 + Az^4 + Bz^3 + Cz^2 + Dz + 36$ given that all its roots are positive integers.
A) -192
B) -180
C) -170
D) -160

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