
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 $f(x)=A\sin (ωx+φ)(A > 0,ω > 0,|φ| < \dfrac {π}{2})$, its graph's first maximum point and minimum point on the right side of the $y$-axis are $(π,2)$ and $(4π,-2)$, respectively.

1. Find the analytical expression of $f(x)$;
2. Shrink the abscissa of all points on the graph of $y=f(x)$ to one-fourth of the original (the ordinate remains unchanged), then move the new graph to the positive direction of the $x$-axis by $\dfrac {π}{3}$ units to obtain the graph of the function $y=g(x)$. Write the analytical expression of $y=g(x)$.

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