
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
Let \(a\), \(b\), and \(c\) be the roots of the polynomial equation
\[x^3 - 5x + 7 = 0.\]
Find the monic polynomial, in \(x\), whose roots are \(a + 3\), \(b + 3\), and \(c + 3\).

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