
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 flock of geese is flying, and a lone goose flies towards them and says, "Hello, a hundred geese!" The leader of the flock responds, "No, we are not a hundred geese! If there were as many of us as there are now, plus the same amount, plus half of that amount, plus a quarter of that amount, plus you, goose, then we would be a hundred geese. But as it is..." How many geese were in the flock?

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