
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 $f(x)$ satisfies $f(1)= \frac {1}{2}$ and for all real numbers $x$, $y$ it holds that $f(x+y) + f(x-y) = 2f(x)f(y)$, find the value of $f(1) + f(2) + f(3) + \dots + f(2013)$.

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