
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 peculiar spinner has three outcomes: green, red, and blue. It lands on green with probability $\frac{1}{4}$, on red with probability $\frac{1}{2}$, and on blue with probability $\frac{1}{4}$. Winning amounts are associated as follows: if it lands on green, you win $2 dollars; if it lands on red, you win $4 dollars; but if it lands on blue, you lose $6 dollars. What is the expected winnings from spinning this spinner?

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