
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 ordered pairs of integers $(a,b)$ satisfy all of the following inequalities?
\[ \begin{aligned} 
a^2 + b^2 &< 25 \\ 
a^2 + b^2 &< 9a \\ 
a^2 + b^2 &< 9b \\ 
a^2 + b^2 &< -9a + 81
\end{aligned} \]

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