
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
(1) On a number line, two points represent the rational numbers $a$ and $b$. Calculate the distance between these two points.  
(2) Does there exist a rational number $x$ such that $|x+1| + |x-3| = x$?  
(3) Does there exist an integer $x$ such that $|x-4| + |x-3| + |x+3| + |x+4| = 14$? If it exists, find all such integers $x$; if not, explain why.

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