
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
If there exists $\triangle ABC$ that satisfies any three of the conditions ①, ②, ③, and ④, please select a set of three conditions and answer the following questions:<br/>$(Ⅰ)$ Find the measure of $\angle A$;<br/>$(Ⅱ)$ Find the values of $\cos B$ and $a$.<br/>Condition ①: $\sin C = \frac{{3\sqrt{3}}}{{14}}$;<br/>Condition ②: $b-a=1$;<br/>Condition ③: $b\cos A = -\frac{5}{2}$;<br/>Condition ④: $a = \frac{7}{3}c$.

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