
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 $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$, respectively, and it satisfies $\cos 2A + 2\sin^2(\pi + B) + 2\cos^2\left(\frac{\pi}{2} + C\right) - 1 = 2\sin B\sin C$.

(Ⅰ) Find the size of angle $A$;

(Ⅱ) If $b=4$ and $c=5$, find $\sin B$.

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