
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 side of the base \(ABCD\) of a regular quadrilateral pyramid \(SABCD\) is \(\frac{8}{\sqrt{7}}\). A plane is drawn through the base of the pyramid's height, parallel to the medians \(SM\) and \(BN\) of the faces \(SAB\) and \(SBC\) respectively. Find the area of the section of the pyramid by this plane, if the distance from the apex of the pyramid to this plane is \(\frac{2}{3}\).

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