
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 alphabet in its natural order  $\text{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$  is  $T_0$ .  We apply a permutation to  $T_0$  to get  $T_1$  which is  $\text{JQOWIPANTZRCVMYEGSHUFDKBLX}$ .  If we apply the same permutation to  $T_1$ , we get  $T_2$  which is  $\text{ZGYKTEJMUXSODVLIAHNFPWRQCB}$ .  We continually apply this permutation to each  $T_m$  to get  $T_{m+1}$ .  Find the smallest positive integer  $n$  so that  $T_n=T_0$ .

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