
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
Definition: If the function $y=f(x)$ ($x \in D$) satisfies (1) $f(x)$ is a monotonic function on $D$; (2) there exists a closed interval $[a, b] \subseteq D$, such that the range of $f(x)$ on the interval $[a, b]$ is also $[a, b]$, then $f(x)$ is called a closed function. Among the following functions:  
(1) $f(x) = x^2 + 2x$, $x \in [-1, +\infty)$; (2) $f(x) = x^3$, $x \in [-2, 3]$; (3) $f(x) = \log x$, $x \in [1, +\infty)$  
The ones that are closed functions are $\boxed{(1) (2)}$.

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