
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 our province, the new college entrance examination adopts a "choose 3 out of 7" model, which means choosing 3 subjects from politics, history, geography, physics, chemistry, biology, and technology as elective subjects. How many possible combinations of elective subjects are there? If person A must choose physics and politics, and person B does not choose technology, how many combinations are there such that both persons have at least one subject in common? (Answer mathematically)

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