
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 $α \in \left( \frac{\pi}{2}, \pi \right)$, and $\sin α = \frac{4}{5}$.  
$(1)$ Find the value of $\cos \left(α - \frac{\pi}{4}\right)$;  
$(2)$ Find the value of $\sin^2 \frac{α}{2} + \frac{\sin 4α \cos 2α}{1+\cos 4α}$.

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