
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 $m=\frac{\tan 22.5^{\circ} }{1-\tan^{2} 22.5^{\circ }}$, find the minimum value of the function $y=2m\cdot x+\frac{3}{x-1}+1$ for $x > 1$.

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