
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
Check if $x=4$ is a root of the polynomial $x^3 - 5x^2 + 7x - 12$. If it is not, find the correct numerical coefficient of $x$ in place of $7$ so that $x=4$ would be a root of the polynomial $x^3 - 5x^2 + ax - 12$.

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