
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 hotel charges a flat fee for the first night and an additional fee for each subsequent night. However, for stays longer than 4 nights, the additional fee per night is reduced by $10$ for those nights exceeding 4. If it costs Martin $\$180$ for a 4-night stay and Alex $\$302$ for a 7-night stay, what is the flat fee for the first night and the regular additional fee per night?

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