
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
From the set {$1$, $2$, $3$, $4$, $5$}, two different numbers are randomly chosen. Let event $A=$ "The product of the two chosen numbers is even", and event $B=$ "Both chosen numbers are even". Compute $P(B|A)=$____.

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