
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
The number of games won by six basketball teams are displayed in the graph, but the names of the teams are missing. The following clues provide information about the teams:

1. The Hawks won more games than the Falcons.
2. The Warriors won more games than the Knights, but fewer games than the Royals.
3. The Knights won more than 30 games.
4. The Squires tied with the Falcons.

How many games did the Warriors win? [asy]
size(150);
defaultpen(linewidth(0.7pt)+fontsize(8));

int i = 1;

draw((0,i*10)--(80,i*10)); ++i;

fill(shift(12,0)*((4,0)--(4,10)--(8,10)--(8,0)--cycle),purple);
draw(shift(12,0)*((4,0)--(4,10)^^(8,0)--(8,10)));
draw((0,i*10)--(80,i*10)); ++i;

fill((4,0)--(4,20)--(8,20)--(8,0)--cycle,purple);
draw((4,0)--(4,20));
draw((8,0)--(8,20));

for(i = 3; i <= 4; ++i)
{
draw((0,i*10)--(80,i*10));
}

fill(shift(24,0)*((4,0)--(4,35)--(8,35)--(8,0)--cycle),purple);
draw(shift(24,0)*((4,0)--(4,35)^^(8,0)--(8,35)));
draw((0,i*10)--(80,i*10)); ++i;

fill(shift(36,0)*((4,0)--(4,40)--(8,40)--(8,0)--cycle),purple);
draw(shift(36,0)*((4,0)--(4,40)^^(8,0)--(8,40)));
draw((0,i*10)--(80,i*10)); ++i;

fill(shift(48,0)*((4,0)--(4,50)--(8,50)--(8,0)--cycle),purple);
draw(shift(48,0)*((4,0)--(4,50)^^(8,0)--(8,50)));
draw((0,i*10)--(80,i*10)); ++i;

fill(shift(60,0)*((4,0)--(4,50)--(8,50)--(8,0)--cycle),purple);
draw(shift(60,0)*((4,0)--(4,50)^^(8,0)--(8,50)));
draw((0,i*10)--(80,i*10));

xaxis(Bottom,0,80,RightTicks(" ",N=6,n=1,Size=2));
yaxis(Left,0,60,LeftTicks(Step=10,Size=2));
yaxis(Right,0,60);

label("Basketball Results",(40,66));
label(rotate(90)*"Number of Wins",(-10,30));
label("Teams",(40,-10));
for(i = 0; i < 6; ++i)
{
label("?",(6+12*i,-4));
}
[/asy]

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