
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
Within a certain range, the purchase quantity $y$ tons of a certain product and the unit price $x$ yuan satisfy a linear function relationship. If 1000 tons are purchased at 800 yuan per ton, and 2000 tons are purchased at 700 yuan per ton, then the unit price for purchasing 400 tons should be ______ yuan.

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