
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 $f(x)= \dfrac {2x}{x+1}$ and the graph of the function $y=g(x)$ is symmetric about the line $x=2$,  
$(1)$ find the expression for $g(x)$;  
$(2)$ If $\Phi(x+2)= \dfrac {1}{\Phi(x)}$ for $x\in(-2,0)$, and $\Phi(x)=g(x)$, find the value of $\Phi(2005)$.

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