
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
Determine the third root of the polynomial equation:
\[
cx^3 + (c - 3d)x^2 + (2d + 4c)x + (12 - 2c) = 0
\]
given that two of its roots are 1 and -3.

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