
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 that $\frac{4\sin \theta-2\cos \theta}{3\sin \theta+5\cos \theta}=\frac{6}{11}$, find the value of the following expressions:

$(1) \frac{5\cos ^{2}\theta}{\sin ^{2}\theta+2\sin \theta\cos \theta-3\cos ^{2}\theta}$;

$(2) 1-4\sin \theta\cos \theta+2\cos ^{2}\theta$.

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