
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 $f(x)=a\sin x+b\cos x$, where $a$ and $b$ are non-zero real constants.
(1) $f( \frac {π}{4})= \sqrt {2}$, and the maximum value of $f(x)$ is $\sqrt {10}$, find the values of $a$ and $b$;
(2) If $a=1$, $x= \frac {π}{6}$ is a symmetry axis of the graph of $f(x)$, find the value of $x_{0}$ that satisfies $f(x_{0})= \sqrt {3}$, and $x_{0} \in [0,2π]$.

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