
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given vectors $\overrightarrow{m}=(\cos (A-B),\sin (A-B))$ and $\overrightarrow{n}=(\cos B,-\sin B)$, with $\overrightarrow{m}\cdot \overrightarrow{n}=- \frac {3}{5}$
(1) Find the value of $\sin A$;
(2) If $a=4 \sqrt {2}$ and $b=5$, find the measure of angle $B$ and the projection of vector $\overrightarrow{BA}$ onto $\overrightarrow{BC}$.

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