
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
The sequence  $\{a_n\}_{n\ge 1}$  of real numbers is defined as follows:  $$ a_1=1, \quad \text{and}\quad a_{n+1}=\frac{1}{2\lfloor a_n \rfloor -a_n+1} \quad \text{for all} \quad n\ge 1 $$  Find  $a_{2024}$ .

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