
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
Charles and Dana live 15 kilometers apart in a straight east-west line, with Charles to the west of Dana. They both observe a kite at the same time, with Charles looking due north and Dana looking directly west. The angle of elevation to the kite from Charles's position is 45° while from Dana’s it is 30°. Determine the altitude of the kite from the ground.
A) $\frac{15\sqrt{3}}{2}$ km
B) $7.5(\sqrt{3} - 1)$ km
C) $7.5(\sqrt{3} + 1)$ km
D) $\frac{15(\sqrt{3} - 1)}{2}$ km
E) 6.5 km

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