
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 vector $\overrightarrow {a}$ is collinear with vector $\overrightarrow {b}$, and $\overrightarrow {b} = (1, -2)$, $\overrightarrow {a} \cdot \overrightarrow {b} = -10$  
(Ⅰ) Find the coordinates of vector $\overrightarrow {a}$;  
(Ⅱ) If $\overrightarrow {c} = (6, -7)$, find $| \overrightarrow {a} + \overrightarrow {c} |$

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