
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 that $f(1,1)=1$, $f(m,n) \in \mathbb{N}^*$, and for any $m, n \in \mathbb{N}^*$, the following conditions hold:
1) $f(m, n+1) = f(m, n) + 2$;
2) $f(m+1, 1) = 2f(m, 1)$.

Determine the correct conclusion(s) from the following three options:
1) $f(1, 5) = 9$;
2) $f(5, 1) = 16$;
3) $f(5, 6) = 26$.

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