
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 $\overrightarrow {a}=(\cosα， \sinα)$ and $\overrightarrow {b}=(\cosβ， -\sinβ)$, where both $α$ and $β$ are acute angles, and $|\overrightarrow {a} - \overrightarrow {b}|= \frac{\sqrt{10}}{5}$,

1. Find the value of $\cos(α+β)$.
2. If $\cosα= \frac{3}{5}$, find the value of $\cosβ$.

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