
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
The distance between points $A$ and $B$ is 500 kilometers. Two cyclists, Alpha and Beta, start from point $A$ to point $B$ at the same time. Alpha cycles 30 kilometers per day, and Beta cycles 50 kilometers per day but rests every other day. At the end of the $\qquad$ day, the remaining distance Beta has to travel to point $B$ is twice the remaining distance Alpha has to travel.

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