
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 $\overrightarrow {a}$ = (4cosα, sinα), $\overrightarrow {b}$ = (sinβ, 4cosβ), and $\overrightarrow {c}$ = (cosβ, -4sinβ)
1. If $\overrightarrow {a}$ is perpendicular to $\overrightarrow {b}$ - 2$\overrightarrow {c}$, find the value of tan(α + β).
2. Find the range of $|\overrightarrow {b} + \overrightarrow {c}|$.

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