
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
Three sides \(OAB, OAC\) and \(OBC\) of a tetrahedron \(OABC\) are right-angled triangles, i.e. \(\angle AOB = \angle AOC = \angle BOC = 90^\circ\). Given that \(OA = 7\), \(OB = 2\), and \(OC = 6\), find the value of
\[
(\text{Area of }\triangle OAB)^2 + (\text{Area of }\triangle OAC)^2 + (\text{Area of }\triangle OBC)^2 + (\text{Area of }\triangle ABC)^2.
\]

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