
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
For \( a, b \in \mathbb{R} \), define \(\max \{a, b\}=\left\{\begin{array}{ll}a, & a \geq b \\ b, & a < b \end{array}\right.\). The minimum value of the function \( f(x) = \max \{|x+1|, |x-2|\} \) for \( x \in \mathbb{R} \) is _____.

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