
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 $\triangle ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to the internal angles $A$, $B$, and $C$, respectively, and $\sin \left(A-B\right)\cos C=\cos B\sin \left(A-C\right)$. <br/>$(1)$ Determine the shape of triangle $\triangle ABC$; <br/>$(2)$ If triangle $\triangle ABC$ is an acute triangle and $a=\frac{1}{\sin B}$, find the maximum value of $\frac{{b}^{2}+{a}^{2}}{(ab)^{2}}$.

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