
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 $\triangle ABC$, $A$, $B$, $C$ correspond to sides $a$, $b$, $c$, and it is known that $acosC + \frac{1}{2}c = b$.
(I) Find angle $A$;
(II) If $b=4$, $c=6$, find the values of $cosB$ and $cos(A+2B)$.

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