
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
In $\triangle ABC$, let $a$, $b$, $c$ be the lengths of the sides opposite angles $A$, $B$, $C$ respectively. Given the vectors $\overrightarrow {m} = (\cos(A-B), \ \sin(A-B))$ and $\overrightarrow {n} = (\cos B, \ -\sin B)$, and that $\overrightarrow {m} \cdot \overrightarrow {n} = -\frac{3}{5}$.  
(Ⅰ) Find the value of $\sin A$;  
(Ⅱ) If $a = 4\sqrt{2}$ and $b = 5$, determine the measure of angle $B$ and the projection of vector $\overrightarrow {AB}$ onto the direction of $\overrightarrow {BC}$.

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