
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
The edge of a regular tetrahedron is $a$. Find the sides and the area of a cross-section that is parallel to two of its skew edges and is at a distance $b$ from the center of the tetrahedron, where $0 < b < \frac{a \sqrt{2}}{4}$.

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