
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 $f(x)=2a\cos ^{2} \frac {x}{2}+2 \sqrt {3}a\sin \frac {x}{2}\cos \frac {x}{2}-a+b$, and $f( \frac {π}{3})=3$, $f( \frac {5π}{6})=1$
(1) Find the values of $a$ and $b$;
(2) Find the range of the function $f(x)$ on $[0, \frac {π}{2}]$.

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