
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
If the integers \( a, b, c \) satisfy \( 0 \leq a \leq 10 \), \( 0 \leq b \leq 10 \), \( 0 \leq c \leq 10 \), and \( 10 \leq a + b + c \leq 20 \), then how many ordered triples \((a, b, c)\) meet the conditions?

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