
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
Let vector $\overrightarrow {a} = (\cos 23°,\cos 67°)$ and vector $\overrightarrow {b} = (\cos 68°,\cos 22°)$.  
(1) Find the dot product $\overrightarrow {a} \cdot \overrightarrow {b}$.  
(2) If vector $\overrightarrow {b}$ is collinear with vector $\overrightarrow {m}$ and $\overrightarrow {u} = \overrightarrow {a} + \overrightarrow {m}$, find the minimum value of the magnitude of vector $\overrightarrow {u}$.

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