
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
**Reading**: The expression $|5-2|$ represents the absolute value of the difference between 5 and 2, which can also be understood as the distance between the points corresponding to 5 and 2 on the number line; $|5+2|$ can be seen as $|5-(-2)|$, representing the absolute value of the difference between 5 and -2, which can also be understood as the distance between the points corresponding to 5 and -2 on the number line.  
**Exploration**:  
(1) If $|x-2|=5$, then $x=$    ;  
(2) Using the number line, find all the integers $x$ that satisfy the condition where the sum of the distances of the point represented by $x$ to the points corresponding to 2 and -1 is 3.  
(3) Based on the above exploration, conjecture whether for any rational number $x$, $|x-2|+|x+3|$ has a minimum value? If it does, write down the minimum value; if it does not, explain why.

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