
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
When \(x\) is divided by each of \(6\), \(7\), and \(8\), remainders of \(5\), \(6\), and \(7\) (respectively) are obtained. What is the smallest possible positive integer value of \(x\)?

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