
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 $\triangle ABC$, $2\cos ^{2} \frac {A-B}{2}\cos B-\sin (A-B)\sin B+\cos (A+C)=- \frac {3}{5}$.
(1) Find the value of $\cos A$;
(2) If $a=4 \sqrt {2}$, $b=5$, find the projection of $\overrightarrow{BA}$ on $\overrightarrow{BC}$.

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