
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
Let $f(x) = \frac{4x^2 + 6x + 9}{x^2 - 2x + 5}$ and $g(x) = x - 2$. Find $f(g(x)) + g(f(x))$, evaluated when $x = 2$.

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