
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
Point $H$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BH$ intersects diagonal $AC$ at $J$ and side $DC$ at $K$. If $JK = 12$ and $KH = 36$, then $BJ = ?$
[asy] size(7cm); pair A = (0, 0), B = (7, 0), C = (10, 5), D = (3, 5), H = (5.7, 9.5); pair K = intersectionpoints(B--H, D--C)[0]; pair J = intersectionpoints(A--C, B--H)[0]; draw(A--D--C--B--cycle); draw(A--C); draw(D--H--B); label("$A$", A, SW); label("$B$", B, SE); label("$C$", C, NE); label("$D$", D, NW); label("$H$", H, N); label("$K$", K, NE); label("$J$", J, SE); //Credit to MSTang for the asymptote[/asy]

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