
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 the function $f(x)=\sin 2x+2\cos ^{2}x+m$.  
$(Ⅰ)$ Find the minimum positive period of the function $f(x)$.  
$(Ⅱ)$ Among the following three conditions, choose one as the given condition to uniquely determine the real number $m$. Then, find the minimum value of the function $f(x)$ on the interval $[0, \frac{π}{2}]$.  
Condition ①: The maximum value of $f(x)$ is $1$;  
Condition ②: A point of symmetry for $f(x)$ is $(\frac{{3π}}{8},0)$;  
Condition ③: A line of symmetry for $f(x)$ is $x=\frac{π}{8}$.

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