
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 the sequence $\{a_{n}\}$, $\frac{1-a_{n+1}}{a_{n+1}}=\frac{1+a_{n}}{a_n}$, and $\frac{1}{a_3}+\frac{1}{a_{15}}=36$.<br/>$(Ⅰ)$ Find the general formula for $\{a_{n}\}$;<br/>$(Ⅱ)$ Let $b_{n}=\frac{a_n^2}{(1-a_n)(1+a_n)}$, the sum of the first $n$ terms of the sequence $\{b_{n}\}$ is $T_{n}$, if $T_{m}=\frac{10}{21}$, find the value of the positive integer $m$.

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