
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
Let  $a$ ,  $b$ , and  $c$  be positive real numbers such that  $a^2+b^2+c^2=989$  and  $(a+b)^2+(b+c)^2+(c+a)^2=2013$ . Find  $a+b+c$ .

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