
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 linear fractional transformation of  $x$  into  $f_1(x)=\dfrac{2x-1}{x+1}$ , define  $f_{n+1}(x)=f_1(f_n(x))$  for  $n=1,2,3,\cdots$ . Express  $f_{28}(x)$  in terms of  $x$ .

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