
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
Let  $ABC$  be an equilateral triangle of area  $1998$  cm $^2$ . Points  $K, L, M$  divide the segments  $[AB], [BC] ,[CA]$ , respectively, in the ratio  $3:4$  . Line  $AL$  intersects the lines  $CK$  and  $BM$  respectively at the points  $P$  and  $Q$ , and the line  $BM$  intersects the line  $CK$  at point  $R$ . Find the area of the triangle  $PQR$ .

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