
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 that \(a\) is a positive integer. If all the roots of the equation
\[ 
x^{3}+(a+17)x^{2}+(38-a)x-56=0
\]
are integers, find the value of \(a\) and the integer roots of the equation.


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