
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 that function $f(x)$ is an even function defined on $R$, and for any $x∈R$, there is $f(x+4)=f(x)$. When $x∈[4,6]$, $f(x)=2^{x}+1$. The inverse function of $f(x)$ on the interval $[-2,0]$ is $f^{-1}(x)$. Find $f^{-1}(19)=$ _____ .

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