
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
It is known that the values of the quadratic polynomial \(a x^{2} + b x + c\) on the interval \([-1,1]\) do not exceed 1 in absolute value. Find the maximum possible value of the sum \(|a| + |b| + |c|\). Let's determine the answer as 3.

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