
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 denoted as $a$, $b$, and $c$ respectively. It is given that $a^2+c^2-b^2=ac$, and $\sqrt{2}b= \sqrt{3}c$.  
(1) Find the measure of angle $A$.  
(2) Let the function $f(x) = 1 + \cos(2x + B) - \cos2x$. Find the maximum value of $f(x)$.

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