
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
To determine the height of a mountain peak, we conducted measurements from three positions, \(A\), \(B\), and \(C\). From point \(A\), the elevation angle to the peak is \(20^{\circ}\), and the direction towards the base of the peak forms an angle of \(93^{\circ}\) with the direction of \(BA\). At point \(B\), the three positions are in a horizontal plane; the segment \(AB\) is \(100 \, \text{m}\), and the segment \(BC\) is \(150 \, \text{m}\), with the angle between them being \(130^{\circ}\). The peak is located within this angular region. From point \(C\), the elevation angle to the peak is \(22^{\circ}\). What can be determined about the height of the peak above the plane of the positions from these measurements?

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