
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
Workers in a factory produce gadgets and gizmos. Each worker takes a constant amount of time to produce either a gadget or a gizmo, but the times are not the same for both products. In one hour, 80 workers can produce 240 gadgets and 160 gizmos. In three hours, 40 workers can produce 180 gadgets and 270 gizmos. In two hours, 100 workers can produce 500 gadgets and $n$ gizmos. Find $n$.

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