
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
Given that the distances from locations A and B to location C are $10km$ and $15km$ respectively, and location A is north-east of location C at an angle of $25^{\circ}$, while location B is south-east of location C at an angle of $35^{\circ}$. Calculate the distance between locations A and B.

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