
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 person has 5 keys, among which 2 can open the door. Now, they randomly pick a key to try to open the door, and if it doesn't work, they discard it. Determine the probability of successfully opening the door exactly on the third attempt.

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