
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 bot is held in orbit by the gravitational force of attraction to the planet, which creates a centripetal acceleration equal to $4 \pi^{2}(2 R) / T^{2}$, where $R$ is the radius of the planet and $T$ is the period of revolution of the bot. From Newton's second law, we have:

$$
m \frac{4 \pi^{2}(2 R)}{T^{2}}=G \frac{m \rho \frac{4}{3} \pi R^{3}}{(2 R)^{2}}, \quad \rho=\frac{24 \pi}{G T^{2}}
$$

Substituting the approximate value of the gravitational constant $G$ and $T = 4 \cdot 60 \cdot 60$ seconds, we get $\rho \approx 6000 \mathrm{kг} / \mathrm{m}^{3}$.

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