
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 $a, b \in \mathbb{R}$, let $\max(a, b) = \begin{cases} a, a \geq b \\ b, a < b \end{cases}$. The minimum value of the function $f(x) = \max(|x + 1|, |x - 2|), x \in \mathbb{R}$ is \_\_\_\_\_\_.

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