
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 following propositions:
(1) In the average rate of change $\frac{\Delta y}{\Delta x}$, $\Delta x$ must be a positive number.
(2) The tangent to a curve at any given point intersects the curve at only one point.
(3) The derivative of $\sin \left(\frac{\pi}{3}\right)$ is $\cos \left(\frac{\pi}{3}\right)$, which equals $\frac{1}{2}$.
(4) If the function $y=f(x)$ is monotonically increasing on the interval $(a, b)$, then $f'(x) \geq 0$.
(5) A continuous function on a closed interval must have a maximum and minimum value.
The true propositions are ____________ (fill in the index numbers only).

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