
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 $\triangle ABC$, where the sides opposite angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, let $S$ be the area of $\triangle ABC$ with the condition $S= \frac { \sqrt {3}}{4}(a^{2}+c^{2}-b^{2})$.
(Ⅰ) Calculate the measure of angle $B$;
(Ⅱ) If sides $a$, $b$, and $c$ form a geometric progression, find the value of $\sin(A)\sin(C)$.

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