
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 $f(x)=\cos (ωx+φ)(ω > 0, -\frac {π}{2} < φ < 0)$ with the smallest positive period of $π$, and $f(\frac {π}{4})= \frac {\sqrt {3}}{2}$.

1. Find the values of $ω$ and $φ$;
2. Find the monotonically increasing interval of $f(x)$;
3. Find the range of $f(x)$ on the interval $[0, \frac {π}{2}]$.

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