
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 $y=f(x)$, for any $x \in \mathbb{R}$, it satisfies $f(x+2)=\frac{1}{f(x)}$. When $x \in (0, 2]$, $f(x)=x$.
(1) Find the analytical expression of $f(x)$ when $x \in (2, 4]$;
(2) If $f(m)=1$, find the value of $m$;
(3) Calculate the sum: $f(1)+f(2)+f(3)+...+f(2015)$.

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