
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 $\overrightarrow {a} = (1, y)$ and $\overrightarrow {b} = (1, -3)$, and it is known that $(2 \overrightarrow {a} + \overrightarrow {b})$ is perpendicular to $\overrightarrow {b}$.
(1) Determine the coordinates of vector $\overrightarrow {a}$;
(2) Find the angle between vector $\overrightarrow {a}$ and vector $\overrightarrow {b}$.

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