
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 $a$, $b$, $c \in \mathbb{R}$. For any real number $x$ that satisfies $|x| \leqslant 1$, we have $|ax^2 + bx + c| \leqslant 1$. Find the maximum possible value of $|a| + |b| + |c|$.

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