
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 a workshop, the workers are tasked to assemble two types of gadgets: gears and cogs. Each worker takes a constant and identical time per gadget type, but different times might be required for each type. In one hour, 120 workers are able to assemble 240 gears and 360 cogs. In two hours, 80 workers can assemble 320 gears and 400 cogs. In four hours, 100 workers can assemble 800 gears and $n$ cogs. Determine the value of $n$.

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