
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
There is a pile of 660 stones on the table. Each turn, you can split any pile into two smaller piles. The sizes of any two piles on the table at the same time must differ by less than a factor of two. What is the maximum number of piles that can be formed?

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