
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

...

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system
Ella has exactly one of each of the first 30 U.S. state quarters. These quarters were released in the same order that the states joined the union. The graph below shows the number of states that joined the union in each distinct decade. Determine the fraction of Ella's 30 quarters that represent states which joined the union during the decades 1790 through 1809. Express your answer as a common fraction.

(note: each space represents 3 states.)

[asy]size(200);
label("1790",(6,0),S);
label("1810",(12,-12),S);
label("1830",(18,0),S);
label("1850",(24,-12),S);
label("1870",(30,0),S);
label("1890",(36,-12),S);
label("1910",(42,0),S);
label("1970",(48,-12),S);
label("to",(6,-4),S);
label("to",(12,-16),S);
label("to",(18,-4),S);
label("to",(24,-16),S);
label("to",(30,-4),S);
label("to",(36,-16),S);
label("to",(42,-4),S);
label("to",(48,-16),S);
label("1809",(6,-8),S);
label("1829",(12,-20),S);
label("1849",(18,-8),S);
label("1869",(24,-20),S);
label("1889",(30,-8),S);
label("1909",(36,-20),S);
label("1929",(42,-8),S);
label("1979",(48,-20),S);
draw((0,0)--(50,0));
draw((0,2)--(50,2));
draw((0,4)--(50,4));
draw((0,6)--(50,6));
draw((0,8)--(50,8));
draw((0,10)--(50,10));
draw((0,12)--(50,12));
draw((0,14)--(50,14));
draw((0,16)--(50,16));
draw((0,18)--(50,18));
fill((4,0)--(8,0)--(8,18)--(4,18)--cycle,gray(0.8));
fill((10,0)--(14,0)--(14,9)--(10,9)--cycle,gray(0.8));
fill((16,0)--(20,0)--(20,12)--(16,12)--cycle,gray(0.8));
fill((22,0)--(26,0)--(26,11)--(22,11)--cycle,gray(0.8));
fill((28,0)--(32,0)--(32,12)--(28,12)--cycle,gray(0.8));
fill((34,0)--(38,0)--(38,9)--(34,9)--cycle,gray(0.8));
fill((40,0)--(44,0)--(44,7)--(40,7)--cycle,gray(0.8));
[/asy]

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