
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 $\triangle ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively. Suppose $a\cos A=b\cos B$.
(1) If $a=3$ and $b=4$, find the value of $| \overrightarrow{CA}+ \overrightarrow{CB}|$.
(2) If $C=60^{\circ}$ and the area of $\triangle ABC$ is $\sqrt {3}$, find the value of $\overrightarrow{AB}\cdot \overrightarrow{BC}+ \overrightarrow{BC}\cdot \overrightarrow{CA}+ \overrightarrow{CA}\cdot \overrightarrow{AB}$.

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