
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 two lighthouses A and B are both at a distance of a km from the ocean observation station C, lighthouse A is located to the northeast of station C at an angle of 20°, and lighthouse B is located to the southeast of station C at an angle of 40°, calculate the distance between lighthouse A and B.

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