
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 game works as follows: the player pays  $2$  tokens to enter the game. Then, a fair coin is flipped. If the coin lands on heads, they receive  $3$  tokens; if the coin lands on tails, they receive nothing. A player starts with  $2$  tokens and keeps playing this game until they do not have enough tokens to play again. What is the expected value of the number of tokens they have left at the end?

*2020 CCA Math Bonanza Team Round #9*

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