
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
A person distributes grains of rice on a chessboard. On each square numbered \( k \), \( 2^k \) grains of rice are placed. How many grains of rice are on the 12th square compared to the total grains on the first 10 squares combined?

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