
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
Let \([x]\) denote the greatest integer less than or equal to the real number \(x\). For example, \([3]=3\), \([2.7]=2\), and \([-2.2]=-3\). Find the last two digits of \(\left[\frac{10^{93}}{10^{31}+3}\right]\).

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