
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
Consider the cubic equation:
\[ax^3 + (a + 4b) x^2 + (b - 5a) x + (10 - a) = 0\]
Given that two of its roots are $-1$ and $4$, find the third root.

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