
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
Trevor and Edward play a game in which they take turns adding or removing beans from a pile. On each turn, a player must either add or remove the largest perfect square number of beans that is in the heap. The player who empties the pile wins. The game starts with a finite number of beans in the pile, fewer than 1000. Edward lets Trevor go first, and Edward wins the game. Find a number \( n \) less than 1000 that would allow this scenario, assuming both players are perfect logicians. A correct answer is worth the nearest integer to \( \log_{2}(n-4) \) points.

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