
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
The "Yancheng Marathon" event has three categories: "Marathon," "Half Marathon," and "Mini Fitness Run." Lele participated in volunteer service work and conducted a survey on some participants to estimate the number of participants in the "Half Marathon" category:

| Number of Surveyed Participants | 20   | 50   | 100  | 200  | 500  | 2000 |
|--------------------------------|------|------|------|------|------|------|
| Number of Participants          | 7    | 20   | 39   | 83   | 209  | 822  |
| Frequency                       | 0.350| 0.400| 0.390| 0.415| 0.418| 0.411|

Please estimate the probability of the number of participants in the "Half Marathon" category in this event to be ________. (Round to $0.01$)

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