
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
Alice and Bob live $12$ miles apart. Alice looks due north to see an airplane and at the same time, Bob looks due northeast to see the same airplane. The angle of elevation of the airplane is $45^\circ$ from Alice's position and $30^\circ$ from Bob's position. Determine the altitude of the airplane in miles.

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