
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
The width of a football field is $a$ meters, and the width of the goal is $b$ meters. In a football match, a winger from team A dribbles the ball along the sideline directly forward. How far from the opponent's baseline should the winger be to shoot in order to achieve the maximum scoring angle, and what is the maximum angle?

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