
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
In the past two years, several provinces have announced reforms to the new college entrance examination. Some provinces have implemented the "$3+1+2$" college entrance examination mode. In this mode, "$3$" refers to the three compulsory subjects of Chinese, Mathematics, and Foreign Language in the national unified college entrance examination. "$1$" refers to one subject that candidates can choose from Physics and History. "$2$" refers to two subjects that candidates can choose from Ideological and Political Education, Geography, Chemistry, and Biology. What is the probability that two candidates, A and B, have exactly two selected subjects in common?

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