
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

Two bear cubs found a large, round piece of cheese. They wanted to split it evenly but couldn't because each one feared the other would get a larger portion. Suddenly, a fox appeared and offered to divide the cheese for them.

- "Let me divide the cheese evenly for you."
- "Great!" exclaimed the bear cubs. "Divide it!"

The fox broke the cheese into two parts, but one piece was larger than the other. The bear cubs protested:
- "This one is bigger!"

The fox reassured them:
- "I'll fix it right now."

The fox bit off a piece from the larger portion, equal in size to the smaller portion. Now the other piece became larger.
- "It's still uneven!" worried the bear cubs.

- "Don't worry," said the fox. "I know what I'm doing!"

She continued to bite off from the larger piece, an amount equal to the smaller piece. She kept dividing the cheese this way until she had eaten enough. She bit off from each portion 3 times, each time taking a piece equal to the other portion. The bear cubs, with their little black noses, watched from one piece to the other.

Finally, the pieces were equal, but there was almost no cheese left for the bear cubs: just two small pieces, each weighing 25 grams.

- "Well," said the fox, "there's not much left, but at least it's fair! Enjoy your meal, little bears!" And with that, the cunning fox ran away. 

Determine the weight of the original piece of cheese found by the bear cubs.

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