
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 biased die has three outcomes: landing on an odd number (1, 3, 5) with probability $\frac{1}{2}$, landing on an even number but not 6 (2, 4) with probability $\frac{1}{3}$, and landing on 6 with probability $\frac{1}{6}$. Gaining a number shows an increase in points by the number landed on, but landing on 6 results in losing 5 points. What is the expected points gain or loss when rolling this die?

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