
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
Given \( f(x) = 3x + 1 \) (where \( x \in \mathbb{R} \)), if \( |f(x) - 4| < a \) holds under the condition \( |x - 1| < b \), where \( a, b \in \mathbb{R}^{+} \), find the relationship that \( a \) and \( b \) must satisfy.

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