
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
Given that $a$ is a rational number, does the algebraic expression $|a-1| + |a-2| + |a-3| + |a-4|$ have a minimum value? If it does, please find this minimum value; if not, please explain why.

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