
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
An unfair die is rolled with a probability of $\frac{5}{6}$ to show a number less than 6, and $\frac{1}{6}$ to show a 6. Rolling any number from 1 to 5 gains \$5, but rolling a 6 loses \$30. What is the expected worth of rolling this die?

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