
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
For the function $y=f(x)$, for any $x \in \mathbb{R}$, it holds that $f(x+2) = \frac{1}{f(x)}$. When $x \in (0, 2]$, $f(x) = x$.

(1) When $x \in (2, 4]$, find the expression for $f(x)$;  
(2) If $f(m) = 1$, find the value of $m$;  
(3) Calculate the sum: $f(1) + f(2) + f(3) + \ldots + f(2015)$.

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