
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
Determine the positive integer parameters \( t, u, v \) such that the function

\[ y = f(x)\left(2^{3u-5v-3}-1\right) x^{2} + \left(2^{7u-8v-18}-2^{4u-3v-15}\right) x + \frac{11t^{2}-5u}{154v-10t^{2}} \]

has a positive minimum at \( x = -\frac{1}{8} \).

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