
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 \(f(x)=\frac{b x+1}{2 x+a} \quad (a, b\) are constants, \(a b \neq 2\)). If \(f(x) \cdot f\left(\frac{1}{x}\right) = k\), then \(k =\) ______ ; If \(f[f(1)] = \frac{k}{2}\), then \(a =\) ______ \(b =\) ______

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