
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 $\overrightarrow {a}$ and $\overrightarrow {b}$ that satisfy $| \overrightarrow {a} |=5$, $| \overrightarrow {b} |=3$, and $( \overrightarrow {a} - \overrightarrow {b} )(2 \overrightarrow {a} + 3 \overrightarrow {b} )=13$.

1. Find the cosine value of the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$.
2. Find the magnitude of $| \overrightarrow {a} + 2 \overrightarrow {b} |$.

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