
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 $2b$ be the width of the field, $2a$ be the width of the goal, and $c$ be the distance to the sideline. Draw a circle through the two goalposts (points $A_{1}$ and $A_{2}$) that is tangent to the line on which the player is running ($B$ is the point of tangency). Then the angle $A_{1} B A_{2}$ is the maximum possible (any other angle equals the corresponding inscribed angle in the circle minus some quantity). The radius of this circle is $b - c$.

By the Pythagorean theorem:
$$(b - c)^{2} = a^{2} + x^{2}$$
where $x$ is the desired distance. Therefore:
$$x = \sqrt{(b - c)^{2} - a^{2}} = \sqrt{16^{2} - 4^{4}} = \sqrt{240} = 4 \sqrt{15} \approx 15.5 \text{ m}$$

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