
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
Equilateral triangle $DEF$ is folded such that vertex $D$ now rests at $D'$ on $\overline{EF}$. If $ED' = 2$ and $D'F = 3$, find the length of the crease $\overline{RS}.$

[asy]
unitsize(1 cm);

pair D, Dp, E, F, R, S;

D = 4*dir(60);
E = (0,0);
F = (5,0);
Dp = (2,0);
R = 12/7*dir(60);
S = F + 9/8*dir(120);

draw(E--F--S--R--cycle);
draw(R--Dp--S);
draw(R--D--S,dashed);

label("$D$", D, N);
label("$D'$", Dp, S);
label("$E$", E, SW);
label("$F$", F, SE);
label("$R$", R, NW);
label("$S$", S, NE);
[/asy]

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