
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 $\sin(α+ \frac {π}{4})= \frac {7 \sqrt {2}}{10}$ and $α∈( \frac {π}{4}， \frac {π}{2})$, find:

1. The value of $\cosα$
2. The maximum and minimum values of the function $f(x)=\cos2x+ \frac {5}{2}\sinα\sin x$

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