
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 integer solutions  $ (x_0$ ,  $ x_1$ ,  $ x_2$ ,  $ x_3$ ,  $ x_4$ ,  $ x_5$ ,  $ x_6)$  does the equation
\[ 2x_0^2\plus{}x_1^2\plus{}x_2^2\plus{}x_3^2\plus{}x_4^2\plus{}x_5^2\plus{}x_6^2\equal{}9\]
have?

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