
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 $ABC$ where the opposing sides of angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $a$, $b$, $c$ form a geometric progression.

(Ⅰ) Determine the range of values for angle $B$;  
(Ⅱ) Let $f(x) = 3\sin x + 4\cos x$, find the maximum value of $f(B)$ and the value of $\tan B$ when $f(B)$ reaches its maximum value.

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