
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 $f(x) = a\log_{2}x + b\log_{3}x + 2$, solve the following problems:
(1) Find the value of $f(1)$;
(2) Find the value of $f(x) + f\left( \frac{1}{x} \right)$;
(3) Calculate the value of $f(1) + f(2) + f(3) + \ldots + f(2013) + f\left( \frac{1}{2} \right) + f\left( \frac{1}{3} \right) + \ldots + f\left( \frac{1}{2013} \right)$.

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