
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 motel offers a discount scheme based on the length of stay. They charge a flat fee for the first night and then a decreased nightly rate after the third night. If it costs Mark $\$310$ to stay for 5 nights and Lucy $\$410$ to stay for 7 nights, determine the flat fee for the first night, and the regular nightly rate before the discount applies, if the discount rate is 20% less than the regular rate.

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