
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
Given the sequence $\left\{a_{n}\right\}$ satisfying: $a_{1}=1, a_{2}=2, a_{2k+1}=\frac{a_{2k}^{2}}{a_{2k-1}}$, and $a_{2k+2}=2a_{2k+1}-a_{2k}$ for $k \in \mathbf{N}^{*}$, find the last two digits of $a_{2022}$.

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