
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 triangle \(ABC\) has sides \(a, b, c\). The altitudes drawn from vertices \(A, B,\) and \(C\) intersect the opposite sides at points \(A_1, B_1, C_1\) respectively. What are the lengths of the sides of triangle \(A_1B_1C_1\)?

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