
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
Suppose $$f(x) = \frac{9^x}{9^x + 3},$$
(1) If $0 < a < 1$, find the value of $f(a) + f(1 - a)$;
(2) Find the value of $$f\left(\frac{1}{1000}\right) + f\left(\frac{2}{1000}\right) + f\left(\frac{3}{1000}\right) + \ldots + f\left(\frac{999}{1000}\right).$$

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