
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
Read the following material:<br/>For real numbers $a$ and $b$, we define the symbol $\min \{a,b\}$ as follows: when $a\geqslant b$, $\min \{a,b\}=b$, for example: $\min \{4,-2\}=-2$, $\min \{5,5\}=5$.<br/>Based on the above material, answer the following questions:<br/>$(1) \min\{-\sqrt{3},-2\}=$______；<br/>$(2)$ When $\min\{\frac{2x-3}{2},\frac{x+2}{3}\}=\frac{x+2}{3}$, find the range of values for $x$.

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