
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 $x, y, z, v, w$ be positive real numbers such that $x^2 + y^2 + z^2 + v^2 + w^2 = 2023$. Let $M$ be the maximum value of
\[xz + 3yz + 2zv + 7zw,\]
and let $x_M, y_M, z_M, v_M, w_M$ be the values of $x, y, z, v, w$ that produce the maximum value of $M$. Find $M + x_M + y_M + z_M + v_M + w_M$.

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