
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 6th sports meeting of Jinzhong City is held in Shouyang. Zhang Fei, the "sports talent" of a high school, excels in the "long jump", "100 meters", "200 meters", and "400 meters" events.<br/>$(1)$ If Zhang Fei randomly chooses one event to participate in, what is the probability that he will choose the "long jump"?<br/>$(2)$ The organizing committee of the sports meeting stipulates that he can participate in at most two events. Using a tree diagram or list method, find the probability that Zhang Fei will choose the "long jump" and "100 meters".

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