
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
Let \( f_{n+1} = \left\{ \begin{array}{ll} f_n + 3 & \text{if } n \text{ is even} \\ f_n - 2 & \text{if } n \text{ is odd} \end{array} \right. \).
If \( f_1 = 60 \), determine the smallest possible value of \( n \) satisfying \( f_m \geq 63 \) for all \( m \geq n \).

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