
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
In the diagram, $\triangle PQR$ is right-angled at $P$ and has $PQ = 3$ and $PR = 3\sqrt{3}$. Altitude $PL$ intersects median $RM$ at $F$. What is the length of $PF$? 
```asy
draw((0,0)--(15,0)--(0,15*sqrt(3))--cycle);
draw((0,0)--(11.25,6.48)); draw((0,15*sqrt(3))--(7.5,0));
draw((10.03,5.79)--(10.76,4.54)--(11.99,5.19));
label("$P$",(0,0),SW); label("$M$",(7.5,0),S); label("$Q$",(15,0),SE);
label("$L$",(11.25,6.48),NE); label("$R$",(0,15*sqrt(3)),N); label("$F$",(6.43,3.7),NW);
```

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