
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 $S=\{(x,y) : x\in \{0,1,2,3\}, y\in \{0,1,2,3,4\}\}$ and $T$ is the set of all right triangles whose vertices are in $S$ and exclude the point $(3,4)$, for every right triangle $t=\triangle{ABC}$ with vertices $A$, $B$, and $C$ in counter-clockwise order and right angle at $B$, let $f(t)=\tan(\angle{ACB})$. Find the product of the function $f(t)$ for all $t$ in $T$.

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