
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 that $a > 0$, the function $f(x)=-2a\sin (2x+ \frac {π}{6})+2a+b$ is such that when $x\in[0, \frac {π}{2}]$, $-5\leqslant f(x)\leqslant 1$.

(1) Find the values of the constants $a$ and $b$.
(2) When $x\in[0, \frac {π}{4}]$, find the maximum and minimum values of $f(x)$ and their corresponding $x$ values.

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