
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
Person A and person B place a piece each at two points on a straight line at a distance \( L \) (where \( L \) is a positive integer). They take turns to move their pieces in either direction along the straight line, with their respective movement distances being \( a \) and \( b \) (where \( a < b \) and both \( a \) and \( b \) are positive integers). If the two pieces meet, person A loses. Determine the necessary and sufficient conditions for person B to have a winning strategy.

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