
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 distance from home to work is \( s = 3 \kappa \) meters. At the moment when Ivan left work, his beloved dog rushed out of the house and ran to meet him. They met at a quarter of the way from work. The dog instantly turned around and ran back home. Reaching home, he instantly turned around again and ran back to his owner, and so on. Assuming Ivan and his dog move at constant speeds, determine the distance the dog will have run by the time Ivan gets home.

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