
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 $y=a\cos x+b (a > 0)$, its maximum value is $3$, and its minimum value is $-1$.

1. Find the values of the real numbers $a$ and $b$.
2. Find the interval where the function $f(x)=b\sin (ax+ \frac {π}{3})$ is monotonically increasing.

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