
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
It is known that the distances from two lighthouses, \\(A\\) and \\(B\\), to a marine observation station \\(C\\) are both \\(3km\\). Lighthouse \\(A\\) is located to the north-east \\(25^{\circ}\\) of station \\(C\\), and lighthouse \\(B\\) is located to the south-east \\(35^{\circ}\\) of station \\(C\\). The distance between lighthouse \\(A\\) and lighthouse \\(B\\) is \_\_\_\_\_\_\_\_.

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