
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
Let the sequence \( x_{1}, x_{2}, x_{3}, \ldots \) satisfy
\[ 3 x_{n} - x_{n-1} = n, \quad n = 2, 3, \ldots \]
and \( \left| x_{1} \right| < 1971 \).

Find \( x_{1971} \), accurate to 0.000001.

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