
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 $f(x)= \frac {ax}{x+b}$, with $f(1)= \frac {5}{4}$ and $f(2)=2$, as well as $f(g(x))=4-x$.

1. Find the explicit formula for $f(x)$.
2. Find the explicit formula for $g(x)$.
3. Calculate the value of $g(5)$.

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