
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
It is known that \(\sqrt{\frac{50+120+130}{2} \times(150-50) \times(150-120) \times(150-130)}=\frac{50 \times 130 \times k}{2}\). If \(t=\frac{k}{\sqrt{1-k^{2}}}\), find the value of \(t\).

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