
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
Let the obtuse triangle $\triangle ABC$ have sides $a$, $b$, and $c$ opposite to the internal angles $A$, $B$, and $C$, respectively. Given that $\frac{{\cos A}}{{1-\sin A}}=\frac{{\cos A+\cos B}}{{1-\sin A+\sin B}}$.<br/>$(Ⅰ)$ If $C=\frac{{2π}}{3}$, find $A$;<br/>$(Ⅱ)$ Find the minimum value of $\frac{{{a^2}+{c^2}}}{{{b^2}}}$.

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