
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 \(a\) and \(b\) be real numbers. For any real number \(x\) satisfying \(0 \leqslant x \leqslant 1\), it holds that \(|ax + b| \leqslant 1\). Find the maximum value of \(|20a + 14b| + |20a - 14b|\).

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