
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 given triangle \( T \), choose a point \( Q \) such that the ratios of the areas of the two parts of the triangle, into which a line \( l \) passing through \( Q \) divides \( T \), are as close as possible.

What will these limits be with the best choice of point \( Q \)?

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