
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 a non-constantly zero function $f(x) = x\log_{2}(ax + \sqrt{ax^{2}+b})$ is an even function.  
(1) Find the values of $a$ and $b$;  
(2) Find the solution set of the inequality $f(x-2) < \log_{2}(1+ \sqrt{2})$.

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