
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 \( y = f(x) \) defined on the interval \([0,1]\) as shown in the graph, for any \( 0 < x_{1} < x_{2} < 1 \), provide the following conclusions:

1. \( f(x_2) - f(x_1) > x_2 - x_1 \)
2. \( x_{2} f(x_{1}) > x_{1} f(x_{2}) \)
3. \( \frac{f(x_1) + f(x_2)}{2} < f\left(\frac{x_1 + x_2}{2}\right) \)

Write the correct conclusion numbers: $\qquad$ . (Fill in all correct conclusion numbers)

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