
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
Show by induction that for all integers $n \geq 1$, $1+\frac{1}{4}+\frac{1}{9}+\ldots+\frac{1}{n^{2}} \leq 2-\frac{1}{n}$. Deduce that this sum is always strictly less than 2.

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