
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
Let  $OABC$  be a tetrahedron such that  $\angle AOB = \angle BOC = \angle COA = 90^\circ$  and its faces have integral surface areas. If  $[OAB] = 20$  and  $[OBC] = 14$ , find the sum of all possible values of  $[OCA][ABC]$ . (Here  $[\triangle]$  denotes the area of  $\triangle$ .)

*Proposed by Robin Park*

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