
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 $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given vectors $\overrightarrow{m} = (a, c)$ and $\overrightarrow{n} = (1 - 2\cos A, 2\cos C - 1)$, with $\overrightarrow{m}$ parallel to $\overrightarrow{n}$:
(I) If $b = 5$, find the value of $a + c$.
(II) If $\tan \frac{B}{2} = \frac{1}{2}$, find the value of $\cos A$.

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