
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 $ABC$ has been creased and folded in such a way that vertex $A$ now touches $A'$ on $\overline{BC}$. Given that $BA' = 2$ units and $A'C = 4$ units, determine the length of the crease $\overline{PQ}$.

[asy]
unitsize(1 cm);

pair A, Ap, B, C, P, Q;

A = 3*dir(60);
B = (0,0);
C = (6,0);
Ap = (2,0);
P = 8/5*dir(60);
Q = C + 5/4*dir(120);

draw(B--C--Q--P--cycle);
draw(P--Ap--Q);
draw(P--A--Q,dashed);

label("$A$", A, N);
label("$A'$", Ap, S);
label("$B$", B, SW);
label("$C$", C, SE);
label("$P$", P, NW);
label("$Q$", Q, NE);
[/asy]

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