
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
According to Moor's Law, the number of shoes in Moor's room doubles every year.  In 2013, Moor's room starts out having exactly one pair of shoes.  If shoes always come in unique, matching pairs, what is the earliest year when Moor has the ability to wear at least 500 mismatches pairs of shoes?  Note that left and right shoes are distinct, and Moor must always wear one of each.

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