
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]


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From the set $\{1,2,3,4,5\}$, two different numbers are randomly chosen. Event $A$ represents "the sum of the two chosen numbers is even", and event $B$ represents "both chosen numbers are even". Calculate the conditional probability $P(B|A)=\_\_\_\_\_\_\_\_\_\_\_\_\_\_$.

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