
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 real numbers $x$ and $y$, we define the symbol $\min \{x,y\}$ as follows: when $x < y$, $\min \{x,y\} = x$; when $x \geq y$, $\min \{x,y\} = y$. For example, $\min \{6,-4\} = -4$, $\min \{4,4\} = 4$, and if $\min \{\frac{{3x-1}}{2}, \frac{{x+1}}{3}\} = \frac{{x+1}}{3}$, then the range of $x$ is ______.

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