
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
Given a function \( f(x) \) defined for all real numbers \( x \) such that for all non-zero values \( x \),
\[ 2f(x) + f\left(\frac{1}{x}\right) = 6x + 3 \]
Let \( T \) denote the sum of all values of \( x \) for which \( f(x) = 2023 \). Compute the integer nearest to \( T \).

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