
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
A function is defined as $y=A\sin (ωx+φ)+c$, where $A > 0, ω > 0, |φ| < \dfrac {π}{2}$. In one period, the highest point of the function is at $(2,2)$, and the lowest point is at $(8,-4)$.

(1) Find the smallest positive period of the function $f(x)$;
(2) Find the interval where the function $f(x)$ is monotonically increasing.

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