
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
Compute the number of tuples \(\left(a_{0}, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right)\) of (not necessarily positive) integers such that \(a_{i} \leq i\) for all \(0 \leq i \leq 5\) and
\[ a_{0} + a_{1} + \cdots + a_{5} = 6. \]

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