
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 $\overrightarrow {a}=3\overrightarrow {e}_1-2\overrightarrow {e}_2$, $\overrightarrow {b}=4\overrightarrow {e}_1+\overrightarrow {e}_2$, where $\overrightarrow {e}_1= (1, 0)$, $\overrightarrow {e}_2= (0, 1)$, determine:
(1) The value of $\overrightarrow {a}\cdot \overrightarrow {b}$ and $|\overrightarrow {a}+\overrightarrow {b}|$;
(2) The cosine of the angle $\theta$ between $\overrightarrow {a}$ and $\overrightarrow {b}$.

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