
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 $k$ purple balls, where $k$ is an unknown positive integer. A ball is drawn at random from the bin. If a green ball is drawn, the player wins 3 dollars, but if a purple ball is drawn, the player loses 1 dollar. The expected amount of money won for playing this game is 1 dollar. What is $k$?

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