
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
A rectangle,  $HOMF$ , has sides  $HO=11$  and  $OM=5$ . A triangle  $\Delta ABC$  has  $H$  as orthocentre,   $O$  as circumcentre,  $M$  be the midpoint of  $BC$ ,  $F$  is the feet of altitude from  $A$ . What is the length of  $BC$  ?

[asy]
unitsize(0.3 cm);
pair F, H, M, O;
F = (0,0);
H = (0,5);
O = (11,5);
M = (11,0);
draw(H--O--M--F--cycle);
label(" $F$ ", F, SW);
label(" $H$ ", H, NW);
label(" $M$ ", M, SE);
label(" $O$ ", O, NE);
[/asy]

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