
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 vectors $\overrightarrow {a}$= (cosα, λsinα) and $\overrightarrow {b}$= (cosβ, sinβ), where λ > 0, 0 < α < β < $\frac {π}{2}$, and $\overrightarrow {a}$+ $\overrightarrow {b}$ is perpendicular to $\overrightarrow {a}$ - $\overrightarrow {b}$.

1. Find the value of the real number λ.
2. If $\overrightarrow {a}$ • $\overrightarrow {b}$ = $\frac {4}{5}$, and tanβ = 2, find the value of tanα.

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