
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 $f(x)+f(\frac{1}{x})$;
3. Calculate the value of $f(1)+f(2)+f(3)+...+f(2013)+f(\frac{1}{2})+f(\frac{1}{3})+...+f(\frac{1}{2013})$.

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