
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
Positive integers  $a$  and  $b$  satisfy  $a^3 + 32b + 2c = 2018$  and  $b^3 + 32a + 2c = 1115$ . Find  $a^2 + b^2 + c^2$ .

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