
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
Emma initially had some coins from her parents, decided to give away one-third of them, and then got one-fourth more coins from her siblings. On her way to a friend's house, she accidentally lost three-fifths of the remaining coins but managed to find half of the coins she lost. What fraction of her original number of coins is still missing after she retraced her steps and found some? Express your answer as a common fraction.

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