
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 $α \in (0, \frac{π}{2})$ and $\sin (\frac{π}{4} - α) = \frac{\sqrt{10}}{10}$,
(1) find the value of $\tan 2α$;
(2) find the value of $\frac{\sin (α + \frac{π}{4})}{\sin 2α + \cos 2α + 1}$.

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