
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 \( P \) be a point inside triangle \( \triangle ABC \), with distances from the sides \( a \), \( b \), and \( c \) denoted as \( r_1 \), \( r_2 \), and \( r_3 \) respectively. Find the point \( P \) that minimizes the value of \( \frac{a}{r_1} + \frac{b}{r_2} + \frac{c}{r_3} \).

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