
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
How many triples  $(a,b,c)$  with  $a,b,c \in \mathbb{R}$  satisfy the following system?  $$ \begin{cases} a^4-b^4=c  b^4-c^4=a  c^4-a^4=b \end{cases} $$  .

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