
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 angles $A$, $B$, and $C$ respectively. Given that $b^{2}+c^{2}-a^{2}=ac\cos C+c^{2}\cos A$.
- (Ⅰ) Find the measure of angle $A$.
- (Ⅱ) If the area of $\triangle ABC$ is $S_{\triangle ABC}=\dfrac{25\sqrt{3}}{4}$ and $a=5$, find $\sin B+\sin C$.

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