
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
(The full score of this question is 14 points)

It is known that the function $f(x)$ defined on the interval $(0, +\infty)$ satisfies $f = f(x_1) - f(x_2)$, and when $x > 1$,

$f(x) < 0$. (1) Find the value of $f(1)$; (2) Determine the monotonicity of $f(x)$

(3) If $f(3) = -1$, solve the inequality $f(|x|) < -2$.

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