
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
In recent years, shared bicycles have gradually become one of the favorite "green travel" methods for college students. Many universities have deployed shared bicycles that can be used on the go with mobile payment. To understand the usage of shared bicycles by students for travel, a certain university randomly sampled the usage of shared bicycles by some students on a particular day and compiled the following statistical table.

| Number of Usages | 0   | 1   | 2   | 3   | 4  | 5  |
|------------------|-----|-----|-----|-----|----|----|
| Number of Students | 22 | 14 | 24 | 27 | 8  | 5  |

$(1)$ The median number of times students used shared bicycles on that day is ______ times, and the mode is ______ times.  
$(2)$ How many times, on average, did each student use shared bicycles on that day?  
$(3)$ If 1500 students from the school travel on a certain day, estimate how many students used shared bicycles three times or more (including 3 times).

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