
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 \( f(x) = ax + b \) (where \( a \) and \( b \) are real numbers), \( f_1(x) = f(x) \), \( f_{n+1}(x) = f(f_n(x)) \) for \( n=1, 2, 3, \cdots \). Given that \( 2a + b = -2 \) and \( f_k(x) = -243x + 244 \), find \( k \).

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