
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 $P$ is taken on the extension of side $LM$ of parallelogram $JKLM$. $JP$ intersects diagonal $KM$ at $Q$ and side $ML$ at $R$. If $QR = 40$ and $RP = 30$, then $JQ$ equals:
[asy] size(7cm); pair J = (0, 0), K = (7, 0), M = (10, 5), L = (3, 5), P = (5.7, 9.5); pair R = intersectionpoints(J--P, L--M)[0]; pair Q = intersectionpoints(K--M, J--P)[0]; draw(J--L--M--K--cycle); draw(K--M); draw(L--P--J); label("$J$", J, SW); label("$K$", K, SE); label("$M$", M, NE); label("$L$", L, NW); label("$P$", P, N); label("$R$", R, NE); label("$Q$", Q, SE); //Credit to MSTang for the asymptote[/asy]

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