
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
Observe the related function graphs and determine the truth of the following propositions.
- $10^x = x$ has real solutions;
- $10^x = x^2$ has real solutions;
- $10^x > x$ for all $x$ in $\mathbb{R}$;
- $10^x > x^2$ for all $x$ in $(0, +\infty)$;
- $10^x = -x$ has two distinct real solutions.
Identify the numbers of the true propositions.

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