
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
Sheep Thievery. Robbers stole $\frac{1}{3}$ of the flock of sheep and $\frac{1}{3}$ of a sheep. Another gang stole $\frac{1}{4}$ of the remaining sheep and $\frac{1}{4}$ of a sheep. Then a third gang of robbers stole $\frac{1}{5}$ of the remaining sheep and an additional $\frac{3}{5}$ of a sheep, after which 409 sheep remained in the flock.

How many sheep were initially in the flock?

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