
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
Let the function $y=f(x)$ be an increasing function defined on $(0, +\infty)$, and satisfy $f(x, y) = f(x) + f(y)$, $f(4) = 1$.

(1) Find the value of $f(1)$;  
(2) If there exists a real number $m$ such that $f(m) = 2$, find the value of $m$;  
(3) If $f(x^2 - 4x - 5) < 2$, find the range of $x$.

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