
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
On the board, the numbers \(1, 2^{1}, 2^{2}, 2^{3}, \ldots, 2^{10}\) are written. You are allowed to erase any two numbers and write their non-negative difference instead. After several such operations, there will be only one number left on the board. What could this number be?

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