
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 stalker, to detect a gravitational anomaly (an area where the acceleration due to gravity changes sharply in magnitude), throws a small nut from the surface of the Earth at an angle \(\alpha = 30^\circ\) to the horizontal with a speed \(v_0 = 20 \, \text{m/s}\). The normal acceleration due to gravity is \(g = 10 \, \text{m/s}^2\). At the highest point of its trajectory, the nut enters the anomaly zone and continues to move in it. As a result, the nut falls to the Earth at a distance of \(S = 15\sqrt{3}\) meters from the stalker. Determine the acceleration due to gravity inside the anomaly. (15 points)

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