
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
To ensure information security, data transmission must be encrypted. The principle of a basic encryption and decryption method is as follows: plaintext $$\xrightarrow{\text{encryption}}$$ ciphertext $$\xrightarrow{\text{transmission}}$$ ciphertext $$\xrightarrow{\text{decryption}}$$ plaintext. Given an encryption process defined by $y=a^{x}-2$ (where $x$ is the plaintext and $y$ is the ciphertext), if the plaintext "3" is encrypted to yield the ciphertext "6", which is then transmitted and decrypted back to plaintext "3", determine the original plaintext corresponding to a received ciphertext of "1022".

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