
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
Given the equation
$$
\begin{array}{l}
x^{4}-16 x^{3}+(81-2 a) x^{2}+(16 a-142) x+ \\
a^{2}-21 a+68=0
\end{array}
$$

where the roots are all integers, find the value of $a$ and solve the equation.

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