
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
In a tetrahedron, all the plane angles at one vertex are right angles. A certain point in space is at a distance of 3 from the mentioned vertex of the tetrahedron and at distances of \(\sqrt{5}\), \(\sqrt{6}\), and \(\sqrt{7}\) from the other vertices of the tetrahedron. Find the distances from the center of the circumscribed sphere of the tetrahedron to each of its faces.

![](https://cdn.mathpix.com/cropped/2024_05_06_1326531d43e0d8faed41g-4.jpg?height=593&width=891&top_left_y=346&top_left_x=274)

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