
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 new insurance policy has been launched by an insurance company that promises to pay out an amount of $a$ if event $E$ occurs within a year. Assuming the probability of $E$ occurring within a year is $p$, in order for the expected revenue of the company to be 10% of $a$, the company should charge the customer an insurance premium of $\_\_\_\_\_\_\_\_$.

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