
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 $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ in $\triangle ABC$, respectively, with $a=4 \sqrt {3}$, $b=6$, and $\cos A=- \frac {1}{3}$.  
(1) Find $c$;  
(2) Find the value of $\cos\left(2B- \frac {\pi}{4}\right)$.

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