
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
Given that $S=\{(x,y) : x\in \{0,1,2,3,4,5\}, y\in \{0,1,2,3,4,5\}\}$, let $T$ be the set of all right triangles whose vertices are in $S$. For every right triangle $t=\triangle{ABC}$ with vertices $A$, $B$, and $C$ in counter-clockwise order and where the right angle can be at any vertex, find the product for all $f(t)=\tan(\angle{CBA})$.

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