
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
You have a whole cake in your pantry. On the first trip to the pantry, you consume one third of the cake. On each successive trip, you eat half of the remaining cake. After six trips to the pantry, what fractional part of the cake have you eaten?

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