
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, while Bob looks due east from his location and sees the same airplane. The angle of elevation from Alice’s perspective is $45^\circ$ and from Bob’s perspective it is $30^\circ$. What is the altitude of the airplane in miles?
A) 4.5 miles
B) 5 miles
C) 5.2 miles
D) 5.5 miles
E) 6 miles

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