
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
If the numbers \(a, A, b\) are in sequence and satisfy \(2A = a + b\), then \(a, A, b\) form an arithmetic sequence. Here, \(A\) is called the arithmetic mean of \(a\) and \(b\). Let \([x]\) represent the greatest integer less than or equal to the real number \(x\), and \(\{x\} + [x] = x\). For a positive real number \(x\), if the three real numbers \(\{x\}, [x], x\) are arranged in some order to form an arithmetic sequence, then \(x =\) ____.

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