
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 the function $f(x) = 6x^2 + x - 1$.

(I) Find the zeros of $f(x)$.
(II) If $\alpha$ is an acute angle, and $\sin\alpha$ is a zero of $f(x)$:
   (i) Calculate the value of $$\frac {\tan(\pi+\alpha) \cdot \cos(-\alpha)}{\cos\left( \frac {\pi}{2}-\alpha \right) \cdot \sin(\pi -\alpha )}$$;
   (ii) Calculate the value of $$\sin\left(\alpha+ \frac {\pi}{6}\right)$$.

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