
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
What is the last digit of the number

\[ 99999^{9999^{999^{99}}}\]

(Exponentiation should start "from the top," i.e., first calculate the number \( n_{1} = 99^{9} \), then compose \( n_{2} = 999^{n_{1}} \), next \( n_{3} = 9999^{n_{2}} \), and finally \( N = 99999^{n_{3}} \).)

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