
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 from her house and sees an airplane. At the same moment, Bob looks due northeast and sees the same airplane. The angle of elevation of the airplane is 45° from Alice's position and 30° from Bob's position. Find the altitude of the airplane.

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