
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
In the mystical mountain, there are only two types of legendary creatures: Nine-Headed Birds and Nine-Tailed Foxes. A Nine-Headed Bird has nine heads and one tail, while a Nine-Tailed Fox has nine tails and one head.

A Nine-Headed Bird discovers that, excluding itself, the total number of tails of the other creatures on the mountain is 4 times the number of heads. A Nine-Tailed Fox discovers that, excluding itself, the total number of tails of the other creatures on the mountain is 3 times the number of heads. How many Nine-Tailed Foxes are there on the mountain?

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