
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
At an observation station $C$, the distances to two lighthouses $A$ and $B$ are $300$ meters and $500$ meters, respectively. Lighthouse $A$ is observed at $30^{\circ}$ north by east from station $C$, and lighthouse $B$ is due west of station $C$. Calculate the distance between the two lighthouses $A$ and $B$.

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