
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 $f(x)=\begin{cases}2 \\\sin \pi x,x < 1 \\f\left(x- \frac{2}{3}\right),x\geqslant 1\end{cases}$, find the value of $\frac{f\left(2\right)}{f\left(- \frac{1}{6}\right)}$ .

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