
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 an obtuse triangle $\triangle ABC$ with angles $A$, $B$, and $C$ and their corresponding opposite sides $a$, $b$, and $c$. It is known that $(\sqrt{2}a - c) \cos B = b \cos C$.

1. Find the measure of angle $B$.
2. Let vector $\overrightarrow{m} = (\cos 2A + 1, \cos A)$ and vector $\overrightarrow{n} = (1, -\frac{8}{5})$, and $\overrightarrow{m} \perp \overrightarrow{n}$. Find the value of $\tan(\frac{\pi}{4} + A)$.

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