
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
A telephone pole that is \(10 \text{ meters}\) tall was struck by lightning and broken into two pieces. The top piece, \(AB\), has fallen down. The top of the pole is resting on the ground, but it is still connected to the main pole at \(B\). The pole is still perpendicular to the ground at \(C\). If the angle between \(AB\) and the flat ground is \(30^\circ\), how high above the ground is the break (that is, what is the length of \(BC\))?

(Note: Image representation of the problem is provided.)

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