
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
Two lighthouses A and B are a distance of $a$ nautical miles and $2a$ nautical miles away from the ocean observation station C, respectively, with lighthouse A located at 35° north by east and lighthouse B located at 25° south by east from the observation station. Calculate the distance between lighthouse A and lighthouse B.

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