
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
Given that Jason flips a fair coin until he sees a head, then wins one gold coin for every tail he flips before the first head, calculate the expected number of gold coins Jason wins at this game.

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