
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 bin contains 8 green balls and $k$ blue balls, where $k$ is an unknown positive integer. A player draws a ball randomly from the bin. The player wins 3 dollars for drawing a green ball and loses 1 dollar for drawing a blue ball. If the expected amount won from playing the game is 1 dollar, what is $k$?

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