
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
Heesu plays a game where he starts with  $1$  piece of candy. Every turn, he flips a fair coin. On heads, he gains another piece of candy, unless he already has  $5$  pieces of candy, in which case he loses  $4$  pieces of candy and goes back to having  $1$  piece of candy. On tails, the game ends. What is the expected number of pieces of candy that Heesu will have when the game ends?

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