
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
Calculate the remainder when 
$$ 1-90\binom{10}{1} + 90^2\binom{10}{2} - 90^3\binom{10}{3} + \ldots +(-1)^k 90^k\binom{10}{k} + \ldots + 90^{10}\binom{10}{10}$$
is divided by $88$.

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