
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
Find all values of the coefficients \(a\), \(b\), and \(c\) of the polynomial

\[ f(x) = x^4 - x^3 + a x^2 + b x + c \]

if it is known that it is divisible by the polynomial \(\varphi(x) = x^3 - 2 x^2 - 5 x + 6\) without remainder.

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