
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
The Hatter, the March Hare, and the Dormouse decided to visit the Duchess, the cook, and the Cheshire Cat. Upon arrival, they found no one at home. In the kitchen, they saw a tray of pretzels. 

The Hatter first ate half of the pretzels and then ate one more. The March Hare ate half of the remaining pretzels and then one more. The Dormouse ate half of the remaining pretzels and then one more. Finally, the Cheshire Cat returned and ate half of the remaining pretzels and then one more, leaving no pretzels on the tray.

How many pretzels were there initially?

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