
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 throws a small nut from the Earth's surface at an angle of $\alpha=30^{\circ}$ to the horizontal with an initial speed $v_{0}=10 \, \mathrm{m}/\mathrm{s}$. The normal acceleration due to gravity is $g=10 \, \mathrm{m}/\mathrm{s}^{2}$. At the highest point of its trajectory, the nut enters a zone of gravitational anomaly (an area where the acceleration due to gravity changes its magnitude sharply), and continues to move within it. As a result, the nut falls to the ground at a distance $S=3 \sqrt{3} \, \mathrm{m}$ 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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