
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
Let \( a_{1}, a_{2}, a_{3} \) be any 3 integers; \( b_{1}, b_{2}, b_{3} \) be any permutation of \( a_{1}, a_{2}, a_{3} \). Then at least one of \( a_{1} - b_{1}, a_{2} - b_{2}, a_{3} - b_{3} \) is even.

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