
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 $\sin 2α = \frac{4}{5}$, $α ∈ (0, \frac{π}{4})$, and $\sin (β - \frac{π}{4}) = \frac{3}{5}$, $β ∈ (\frac{π}{4}, \frac{π}{2})$.
(1) Find the values of $\sin α$ and $\cos α$;
(2) Find the value of $\tan (α + 2β)$.

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