
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
A sequence  $a_1, a_2, \ldots$  satisfies  $a_1 = \dfrac 52$  and  $a_{n + 1} = {a_n}^2 - 2$  for all  $n \ge 1.$  Let  $M$  be the integer which is closest to  $a_{2023}.$  The last digit of  $M$  equals  $$ \mathrm a. ~ 0\qquad \mathrm b.~2\qquad \mathrm c. ~4 \qquad \mathrm d. ~6 \qquad \mathrm e. ~8 $$  

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