
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  $T$  be a triangle with side lengths 3, 4, and 5.  If  $P$  is a point in or on  $T$ , what is the greatest possible sum of the distances from  $P$  to each of the three sides of  $T$ ?

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