
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 a triangle $\triangle ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively. If $\cos A= \frac {3}{4}$, $\cos C= \frac {1}{8}$,
(I) find the ratio $a:b:c$;
(II) if $| \overrightarrow{AC}+ \overrightarrow{BC}|= \sqrt {46}$, find the area of $\triangle ABC$.

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