
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
Two brothers raised a flock of sheep. When the price of each sheep (in yuan) exactly equals the number of sheep in the flock, they sold all the sheep and divided the money equally between them: the elder brother first took 10 yuan, then the younger brother took 10 yuan; they continued this way alternately. In the end, the elder brother took 10 yuan first, and the younger brother took less than 10 yuan. At this point, the elder brother gave his straw hat to the younger brother, making the amount of money they each got equal. How much is the straw hat worth?

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