
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
1. The contrapositive of the proposition "If $x^2-3x+2=0$, then $x=1$" is "If $x \neq 1$, then $x^2-3x+2 \neq 0$";
2. If both P and Q are false propositions, then P and Q are both false propositions;
3. In $\triangle ABC$, the necessary and sufficient condition for $\sin A > \sin B$ is $A > B$;
4. The solution set of the inequality $|x|+|x-1|>a$ is $\mathbb{R}$, then $a \leq 1$;
5. The image of the point $(x, y)$ under the mapping $f$ is $(2^x, \log_{\frac{1}{2}}^y)$, then under the action of $f$, the pre-image of the point $(1, -1)$ is $(0, 2)$.

Among these, the true propositions are __________ (Write down the numbers of all true propositions).

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