
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 lengths of the three sides  $a, b, c$  with  $a \le b \le c$ , of a right triangle is an integer. Find all the sequences  $(a, b, c)$  so that the values of perimeter and area of the triangle are the same.

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