
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 student calligraphy and painting competition with the theme of "Inheriting the Spirit of May Fourth, Creating a Youthful Chapter" was organized by the Student Union of a certain school. Several first, second, and third prize works were awarded. The number of second and third prize works is the same. The distribution of works from the senior year students is $40\%$, $40\%$, and $60\%$ for the first, second, and third prizes respectively. Now, if one piece is randomly selected from the prize-winning works, let $A$ be the event "selecting a first prize work" and $B$ be the event "selecting a prize-winning work from a senior year student." If $P(AB)=0.16$, then $P(A|B)=\_\_\_\_\_\_$.

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