
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
A clothing factory produces a certain type of trench coat. The relationship between the monthly production quantity $x$ (pieces) and the selling price $P$ (yuan/piece) is given by $P = 160 - 2x$. The total cost $R$ of producing $x$ pieces is $R = 500 + 30x$ (yuan). Assuming that all the trench coats produced in a month are sold out, what should the monthly production quantity be for the factory to obtain a monthly profit of at least 1300 yuan?

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