
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 \(\{a_n\}\) is defined by \(a_1=1\) and \(4a_n a_{n+1} = (a_n + a_{n+1} - 1)^2\) with \(a_n > a_{n-1}\), determine the explicit formula for the sequence \(\{a_n\}\).

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