
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 offered by a certain insurance company pays out a sum of $a$ yuan if event $E$ occurs within a year. Given that the probability of $E$ happening within a year is $1\%$, to ensure that the expected profit for the company equals $10\%$ of $a$, the insurance premium that the company should charge its customers is $\_\_\_\_$ yuan. (Express your answer as an algebraic expression involving $a$).

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