
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
The polynomial
\[ ax^4 + bx^3 + cx^2 + dx + e = 0 \]
has coefficients that are all integers, and has roots $-3, 6, 10,$ and $-\frac{1}{4}$. If $e$ is a positive integer, what is its smallest possible value?

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