
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 an infinite sequence of squares with side lengths $a_{1}, a_{2}, \ldots, a_{n}, \ldots$, is it true that if the sequence

$$
S_{n} = a_{1}^{2} + a_{2}^{2} + \ldots + a_{n}^{2}
$$

is convergent, then there exists a larger square in which these given squares can be placed without overlapping?

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