
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

On the parabola \( y = x^2 - 4x - 1 \), three distinct points \( A(x_a, y_a) \), \( B(x_b, y_b) \), and \( C(x_c, y_c) \) are taken. It is known that \( x_c = 5 \) and \( y_a = y_b \). Find the x-coordinate of the intersection of the medians of the triangle \( ABC \).

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