
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 vectors $$\overrightarrow {a}$$, $$\overrightarrow {b}$$, and $$\overrightarrow {c}$$ are in the same plane, and $$\overrightarrow {a}$$ = (1, 2).
1. If |$$\overrightarrow {c}$$| = 2$$\sqrt {5}$$ and $$\overrightarrow {c}$$ is parallel to $$\overrightarrow {a}$$, find $$\overrightarrow {c}$$;
2. If |$$\overrightarrow {b}$$| = $$\frac { \sqrt {5}}{2}$$ and ($$\overrightarrow {a}$$ + 2$$\overrightarrow {b}$$) is perpendicular to (2$$\overrightarrow {a}$$ - $$\overrightarrow {b}$$), find the angle between $$\overrightarrow {a}$$ and $$\overrightarrow {b}$$.

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