
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
Right triangular prism  $ABCDEF$  with triangular faces  $\vartriangle ABC$  and  $\vartriangle DEF$  and edges  $\overline{AD}$ ,  $\overline{BE}$ , and  $\overline{CF}$  has  $\angle ABC = 90^o$  and  $\angle EAB = \angle CAB = 60^o$  . Given that  $AE = 2$ , the volume of  $ABCDEF$  can be written in the form  $\frac{m}{n}$  , where  $m$  and  $n$  are relatively prime positive integers. Compute  $m + n$ .
![Image](https://cdn.artofproblemsolving.com/attachments/4/7/25fbe2ce2df50270b48cc503a8af4e0c013025.png)

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