
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
If \(2 a t^{2}+12 t+9=0\) has equal roots, find \(a\).

If \(a x+b y=1\) and \(4 x+18 y=3\) are parallel, find \(b\).

The \(b\text{-th}\) prime number is \(p\). Find \(p\).

If \(k=\frac{4 \sin \theta+3 \cos \theta}{2 \sin \theta-\cos \theta}\) and \(\tan \theta=3\), find \(k\).

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