
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
In the Cartesian coordinate plane $xOy$, a line is drawn through point P(1, 4) that is tangent to the circle C: $(x - m)^2 + y^2 = m^2 + 5$ ($1 < m < 6$). The tangent points are A and B. The line AB passes through a fixed point; find the coordinates of this point.

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