
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
David drives from his home to the airport to catch a flight.  He drives $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed.  He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early.  Determine the distance from David's home to the airport.

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