
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 \(a, b \in \mathbf{R}\) with \(a < b\). Define the function \( g(x) = \max_{a \leq t \leq b} |x + t| \) for \( x \in \mathbf{R} \), where \(\max_{a \leq t \leq b}\) represents the maximum value of the expression \(|x + t|\) when \( t \in [a, b] \) for \( x \in \mathbf{R} \). What is the minimum value of \( g(x) \)?

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