
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 angles opposite to sides a, b, and c of triangle ABC, respectively, and vectors $$\overrightarrow {m} = (\sin A, \sin B)$$, $$\overrightarrow {n} = (\cos B, \cos A)$$, and $$\overrightarrow {m} \cdot \overrightarrow {n} = \sin 2C$$.  
(1) Find the size of angle C;  
(2) If $\sin A$, $\sin C$, $\sin B$ form an arithmetic sequence, and $$\overrightarrow {CA} \cdot (\overrightarrow {AB} - \overrightarrow {AC}) = 18$$, find the length of side c.

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