
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
For a certain type of savings account that calculates interest using compound interest, if the principal is $a$ yuan, the interest rate per period is $r$, suppose the number of periods is $x$, and the total amount (principal plus interest) is $y$ yuan,
(1) Write the function that describes the relationship between the total amount $y$ and the period $x$;
(2) If a principal of 1000 yuan is deposited and the periodic interest rate is 2.25%, calculate the total amount after 4 periods (given that $1.0225^4 = 1.09308$ and $1.0225^5 = 1.11768$).

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