
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
Three mathematicians and four physicists are standing in two rows for a photo, with three people in the front row and four in the back row. If the mathematicians must stand next to each other, calculate the number of different ways they can arrange themselves.

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