
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 $\triangle ABC$ with internal angles $A$, $B$, $C$ and their corresponding sides $a$, $b$, $c$, such that $(a-b)(\sin A+\sin B)=(a-c)\sin C$.
(1) Find the measure of angle $B$;
(2) If $b=3$, find the maximum value of the altitude $h$ on edge $AC$.

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