
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 set $E = \{x | x \text{ is a positive integer less than } 6\}$, $F = \{x | (x-1)(x-2) = 0\}$, $G = \{a, a^2+1\}$,  
(Ⅰ) Find: $E \cap F$, $E \cup F$.  
(Ⅱ) If $F \subseteq G$ and $G \subseteq F$, find the value of the real number $a$.

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