
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
Given a space station with two living modules attached to a central hub on opposite sides of the hub by long corridors of equal length, each containing $N$ astronauts of equal mass, calculate the ratio of the gravitational field strength $g'$  of the remaining astronauts to the gravitational field strength $g$  of the astronauts before two astronauts from each module climbed into the central hub.

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