
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
Sarah has a collection of the first 30 state quarters released according to the sequence in which states joined the union. A graph shows how many states joined the union in each decade. How many of Sarah's quarters represent states that joined the union during the decade 1790 through 1799? Express your answer as a common fraction.

[asy]size(200);
label("1790",(10,0),S);
label("1810",(20,-12),S);
label("1830",(30,0),S);
label("1850",(40,-12),S);
label("1870",(50,0),S);
label("1890",(60,-12),S);
label("1910",(70,0),S);
label("1960",(80,-12),S);
label("to",(10,-4),S);
label("to",(20,-16),S);
label("to",(30,-4),S);
label("to",(40,-16),S);
label("to",(50,-4),S);
label("to",(60,-16),S);
label("to",(70,-4),S);
label("to",(80,-16),S);
label("1799",(10,-8),S);
label("1809",(20,-20),S);
label("1829",(30,-8),S);
label("1849",(40,-20),S);
label("1869",(50,-8),S);
label("1889",(60,-20),S);
label("1909",(70,-8),S);
label("1959",(80,-20),S);
draw((0,0)--(90,0));
draw((0,2)--(90,2));
draw((0,4)--(90,4));
draw((0,6)--(90,6));
draw((0,8)--(90,8));
draw((0,10)--(90,10));
draw((0,12)--(90,12));
draw((0,14)--(90,14));
draw((0,16)--(90,16));
draw((0,18)--(90,18));
fill((8,0)--(12,0)--(12,6)--(8,6)--cycle,gray(0.8));
fill((18,0)--(22,0)--(22,8)--(18,8)--cycle,gray(0.8));
fill((28,0)--(32,0)--(32,7)--(28,7)--cycle,gray(0.8));
fill((38,0)--(42,0)--(42,6)--(38,6)--cycle,gray(0.8));
fill((48,0)--(52,0)--(52,7)--(48,7)--cycle,gray(0.8));
fill((58,0)--(62,0)--(62,5)--(58,5)--cycle,gray(0.8));
fill((68,0)--(72,0)--(72,4)--(68,4)--cycle,gray(0.8));
[/asy]

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