
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
Among the following five propositions:
① "If p then q" and "If ¬q then ¬p" are contrapositive propositions of each other.
② $am^2 < bm^2$ is a necessary and sufficient condition for $a < b$.
③ The negation of the proposition "The diagonals of a rectangle are equal in length" is false.
④ The roots of the equation $2x^2 - 5x + 2 = 0$ can respectively represent the eccentricities of an ellipse and a hyperbola.
⑤ The directrix equation of the parabola $y = 4x^2$ is $y = -1$.
The true propositions are numbered _______ (write down all the numbers of the true propositions).

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