
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 "x<sup>2</sup>=1" is a sufficient but not necessary condition for "x=1";
② "x=-1" is a necessary but not sufficient condition for "x<sup>2</sup>-3x+2=0";
③ The negation of the proposition "There exists an x in R such that x<sup>2</sup>+x+1<0" is "For all x in R, x<sup>2</sup>+x+1≥0";
④ The contrapositive of the proposition "If x=y, then sinx=siny" is true;
Among these, the true propositions are . (Fill in the numbers of the propositions you think are correct)

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